<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: transparent;
      color: #1e2945;
      padding: 10px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 10px;
    }
    .cards-row {
      display: flex;
      flex-direction: row;
      flex-wrap: wrap;
      justify-content: center;
      gap: 12px;
      width: 100%;
      max-width: 680px;
    }
    .graph-card {
      flex: 1 1 290px;
      max-width: 330px;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 10px 10px 8px;
      display: flex;
      flex-direction: column;
      align-items: center;
    }
    .card-title {
      font-size: 14px;
      font-weight: 700;
      margin-bottom: 2px;
      display: flex;
      align-items: center;
      gap: 6px;
    }
    .card-title.growth { color: #2563eb; }
    .card-title.decay { color: #7c3aed; }
    .eq-badge {
      font-size: 12px;
      font-weight: 600;
      padding: 1px 6px;
      border-radius: 4px;
      margin-bottom: 4px;
    }
    .growth .eq-badge { background: #eff6ff; color: #1d4ed8; }
    .decay .eq-badge { background: #f5f3ff; color: #6d28d9; }
    svg {
      width: 100%;
      height: auto;
      max-height: 200px;
      display: block;
      overflow: visible;
    }
    .axis-line { stroke: #cbd5e1; stroke-width: 1.5; }
    .grid-line { stroke: #f1f5f9; stroke-width: 1; }
    .asymptote { stroke: #ef4444; stroke-width: 1.5; stroke-dasharray: 4, 3; }
    .tick-label { font-size: 10px; fill: #94a3b8; text-anchor: middle; font-family: monospace; }
    .asymptote-label { font-size: 9px; fill: #dc2626; font-weight: 600; }
    .intercept-label { font-size: 10px; font-weight: 700; }
    .tracker-dot { transition: cx 0.15s ease-out, cy 0.15s ease-out; }
    
    /* Interactive Controller */
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 20px;
      padding: 6px 14px;
      width: 100%;
      max-width: 480px;
    }
    .ctrl-label {
      font-size: 12px;
      font-weight: 600;
      color: #475569;
      white-space: nowrap;
    }
    input[type="range"] {
      flex: 1;
      accent-color: #2563eb;
      cursor: pointer;
      height: 6px;
    }
    .btn-group {
      display: flex;
      gap: 4px;
    }
    .step-btn {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      border-radius: 4px;
      padding: 2px 6px;
      font-size: 11px;
      font-weight: 600;
      color: #334155;
      cursor: pointer;
    }
    .step-btn:hover { background: #f1f5f9; }
    .step-btn.active {
      background: #2563eb;
      color: #fff;
      border-color: #2563eb;
    }
  </style>
</head>
<body>

  <div class="cards-row">
    
    <div class="graph-card growth">
      <div class="card-title growth">
        <span>Exponential Growth</span>
        <span style="font-size: 11px; font-weight: 600; color: #64748b;">(b &gt; 1)</span>
      </div>
      <div class="eq-badge">y = 2<sup>x</sup></div>
      <svg id="svgGrowth" viewBox="0 0 280 205">
        
        <line class="grid-line" x1="40" y1="130" x2="260" y2="130" />
        <line class="grid-line" x1="40" y1="98" x2="260" y2="98" />
        <line class="grid-line" x1="40" y1="66" x2="260" y2="66" />
        <line class="grid-line" x1="40" y1="34" x2="260" y2="34" />
        
        <line class="grid-line" x1="75" y1="20" x2="75" y2="180" />
        <line class="grid-line" x1="110" y1="20" x2="110" y2="180" />
        <line class="grid-line" x1="180" y1="20" x2="180" y2="180" />
        <line class="grid-line" x1="215" y1="20" x2="215" y2="180" />
        <line class="grid-line" x1="250" y1="20" x2="250" y2="180" />

        
        <line class="axis-line" x1="30" y1="162" x2="265" y2="162" />
        <line class="axis-line" x1="145" y1="190" x2="145" y2="15" />
        <polygon points="268,162 262,159 262,165" fill="#cbd5e1" />
        <polygon points="145,10 142,16 148,16" fill="#cbd5e1" />

        
        <text class="tick-label" x="145" y="174">0</text>
        <text class="tick-label" x="180" y="174">1</text>
        <text class="tick-label" x="215" y="174">2</text>
        <text class="tick-label" x="110" y="174">-1</text>
        <text class="tick-label" x="75" y="174">-2</text>
        
        <text class="tick-label" x="135" y="133" style="text-anchor: end;">1</text>
        <text class="tick-label" x="135" y="101" style="text-anchor: end;">2</text>
        <text class="tick-label" x="135" y="37" style="text-anchor: end;">4</text>

        
        <line class="asymptote" x1="30" y1="162" x2="265" y2="162" />
        <text class="asymptote-label" x="35" y="156">Asymptote: y = 0</text>

        
        <path id="curveGrowth" fill="none" stroke="#2563eb" stroke-width="2.5" stroke-linecap="round" />

        
        <circle cx="145" cy="130" r="3.5" fill="#2563eb" />
        <text class="intercept-label" x="153" y="127" fill="#1d4ed8">(0, 1)</text>

        
        <circle id="dotGrowth" class="tracker-dot" cx="145" cy="130" r="5" fill="#2563eb" stroke="#ffffff" stroke-width="2" />
        <text id="valGrowth" font-size="10" font-weight="700" fill="#2563eb" x="145" y="112" text-anchor="middle">(0, 1)</text>
      </svg>
    </div>

    
    <div class="graph-card decay">
      <div class="card-title decay">
        <span>Exponential Decay</span>
        <span style="font-size: 11px; font-weight: 600; color: #64748b;">(0 &lt; b &lt; 1)</span>
      </div>
      <div class="eq-badge">y = (0.5)<sup>x</sup></div>
      <svg id="svgDecay" viewBox="0 0 280 205">
        
        <line class="grid-line" x1="40" y1="130" x2="260" y2="130" />
        <line class="grid-line" x1="40" y1="98" x2="260" y2="98" />
        <line class="grid-line" x1="40" y1="66" x2="260" y2="66" />
        <line class="grid-line" x1="40" y1="34" x2="260" y2="34" />
        
        <line class="grid-line" x1="75" y1="20" x2="75" y2="180" />
        <line class="grid-line" x1="110" y1="20" x2="110" y2="180" />
        <line class="grid-line" x1="180" y1="20" x2="180" y2="180" />
        <line class="grid-line" x1="215" y1="20" x2="215" y2="180" />
        <line class="grid-line" x1="250" y1="20" x2="250" y2="180" />

        
        <line class="axis-line" x1="30" y1="162" x2="265" y2="162" />
        <line class="axis-line" x1="145" y1="190" x2="145" y2="15" />
        <polygon points="268,162 262,159 262,165" fill="#cbd5e1" />
        <polygon points="145,10 142,16 148,16" fill="#cbd5e1" />

        
        <text class="tick-label" x="145" y="174">0</text>
        <text class="tick-label" x="180" y="174">1</text>
        <text class="tick-label" x="215" y="174">2</text>
        <text class="tick-label" x="110" y="174">-1</text>
        <text class="tick-label" x="75" y="174">-2</text>
        
        <text class="tick-label" x="135" y="133" style="text-anchor: end;">1</text>
        <text class="tick-label" x="135" y="101" style="text-anchor: end;">2</text>
        <text class="tick-label" x="135" y="37" style="text-anchor: end;">4</text>

        
        <line class="asymptote" x1="30" y1="162" x2="265" y2="162" />
        <text class="asymptote-label" x="175" y="156">Asymptote: y = 0</text>

        
        <path id="curveDecay" fill="none" stroke="#7c3aed" stroke-width="2.5" stroke-linecap="round" />

        
        <circle cx="145" cy="130" r="3.5" fill="#7c3aed" />
        <text class="intercept-label" x="153" y="127" fill="#6d28d9">(0, 1)</text>

        
        <circle id="dotDecay" class="tracker-dot" cx="145" cy="130" r="5" fill="#7c3aed" stroke="#ffffff" stroke-width="2" />
        <text id="valDecay" font-size="10" font-weight="700" fill="#7c3aed" x="145" y="112" text-anchor="middle">(0, 1)</text>
      </svg>
    </div>
  </div>

  
  <div class="controls">
    <span class="ctrl-label">Explore x:</span>
    <input type="range" id="xSlider" min="-2.2" max="2.2" step="0.1" value="0">
    <div class="btn-group">
      <button class="step-btn" data-x="-2">-2</button>
      <button class="step-btn" data-x="-1">-1</button>
      <button class="step-btn active" data-x="0">0</button>
      <button class="step-btn" data-x="1">1</button>
      <button class="step-btn" data-x="2">2</button>
    </div>
  </div>

  <script>
    // Coordinate mapping parameters:
    // Origin (0, 0) is at SVG coordinates (145, 162)
    // 1 unit along X = 35 px
    // 1 unit along Y = 32 px
    const originX = 145;
    const originY = 162;
    const scaleX = 35;
    const scaleY = 32;

    function mathToSvg(x, y) {
      return {
        x: originX + x * scaleX,
        y: originY - y * scaleY
      };
    }

    // Generate accurate mathematical curve paths
    function buildPath(fn, minX, maxX, step) {
      let d = "";
      for (let x = minX; x <= maxX + 0.001; x += step) {
        const y = fn(x);
        const pt = mathToSvg(x, y);
        if (x === minX) {
          d += `M ${pt.x.toFixed(2)} ${pt.y.toFixed(2)}`;
        } else {
          d += ` L ${pt.x.toFixed(2)} ${pt.y.toFixed(2)}`;
        }
      }
      return d;
    }

    const pathGrowth = buildPath(x => Math.pow(2, x), -3.0, 2.22, 0.05);
    const pathDecay  = buildPath(x => Math.pow(0.5, x), -2.22, 3.0, 0.05);

    document.getElementById('curveGrowth').setAttribute('d', pathGrowth);
    document.getElementById('curveDecay').setAttribute('d', pathDecay);

    // Dynamic Inspector
    const slider = document.getElementById('xSlider');
    const dotGrowth = document.getElementById('dotGrowth');
    const dotDecay = document.getElementById('dotDecay');
    const valGrowth = document.getElementById('valGrowth');
    const valDecay = document.getElementById('valDecay');
    const buttons = document.querySelectorAll('.step-btn');

    function updatePoints(xVal) {
      const x = parseFloat(xVal);
      
      // Growth: y = 2^x
      const yG = Math.pow(2, x);
      const ptG = mathToSvg(x, yG);
      dotGrowth.setAttribute('cx', ptG.x);
      dotGrowth.setAttribute('cy', ptG.y);
      valGrowth.setAttribute('x', ptG.x);
      valGrowth.setAttribute('y', ptG.y - 8);
      valGrowth.textContent = `(${x.toFixed(1)}, ${yG.toFixed(2)})`;

      // Decay: y = 0.5^x
      const yD = Math.pow(0.5, x);
      const ptD = mathToSvg(x, yD);
      dotDecay.setAttribute('cx', ptD.x);
      dotDecay.setAttribute('cy', ptD.y);
      valDecay.setAttribute('x', ptD.x);
      valDecay.setAttribute('y', ptD.y - 8);
      valDecay.textContent = `(${x.toFixed(1)}, ${yD.toFixed(2)})`;

      // Sync button states
      buttons.forEach(btn => {
        if (Math.abs(parseFloat(btn.dataset.x) - x) < 0.05) {
          btn.classList.add('active');
        } else {
          btn.classList.remove('active');
        }
      });
    }

    slider.addEventListener('input', (e) => {
      updatePoints(e.target.value);
    });

    buttons.forEach(btn => {
      btn.addEventListener('click', () => {
        const val = btn.dataset.x;
        slider.value = val;
        updatePoints(val);
      });
    });

    // Initial positioning
    updatePoints(0);
  </script>
</body>
</html>

Introduction to Exponential Functions and Their Graphs

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, sans-serif;
      color: #1e2945;
      background: #ffffff;
      padding: 12px;
      display: flex;
      flex-direction: column;
      gap: 10px;
    }

    .header-bar {
      display: flex;
      justify-content: space-between;
      align-items: center;
      flex-wrap: wrap;
      gap: 8px;
    }
    .func-tag {
      font-weight: 700;
      font-size: 17px;
      color: #7c3aed;
      background: #f5f3ff;
      padding: 4px 10px;
      border-radius: 6px;
      border: 1px solid #ddd6fe;
    }
    .controls {
      display: flex;
      gap: 6px;
      align-items: center;
    }
    .btn-step {
      background: #f8fafc;
      border: 1px solid #cbd5e1;
      color: #334155;
      padding: 4px 10px;
      border-radius: 6px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      user-select: none;
      transition: background 0.2s, color 0.2s, border-color 0.2s;
    }
    .btn-step:hover {
      background: #ede9fe;
      border-color: #a78bfa;
      color: #6d28d9;
    }
    .btn-play {
      background: #7c3aed;
      border: 1px solid #6d28d9;
      color: #ffffff;
      padding: 4px 12px;
      border-radius: 6px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      user-select: none;
      transition: opacity 0.2s;
    }
    .btn-play:hover { opacity: 0.9; }

    .main-layout {
      display: grid;
      grid-template-columns: 1.15fr 1fr;
      gap: 12px;
      align-items: center;
    }
    @media (max-width: 520px) {
      .main-layout {
        grid-template-columns: 1fr;
      }
    }

    /* Left Table / Steps */
    .calc-list {
      display: flex;
      flex-direction: column;
      gap: 6px;
    }
    .calc-row {
      display: flex;
      align-items: center;
      justify-content: space-between;
      padding: 6px 10px;
      border-radius: 6px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      font-size: 13px;
      font-variant-numeric: tabular-nums;
      cursor: pointer;
      transition: background 0.25s, border-color 0.25s, box-shadow 0.25s;
    }
    .calc-row.active {
      background: #f5f3ff;
      border-color: #7c3aed;
      box-shadow: 0 0 0 1px #7c3aed;
      font-weight: 600;
    }
    .calc-row .x-val {
      color: #64748b;
      min-width: 48px;
    }
    .calc-row.active .x-val {
      color: #7c3aed;
    }
    .calc-row .math-expr {
      color: #334155;
      letter-spacing: -0.2px;
    }
    .calc-row .y-res {
      font-weight: 700;
      color: #0f172a;
      min-width: 24px;
      text-align: right;
    }
    .calc-row.active .y-res {
      color: #7c3aed;
    }

    /* Graph Container */
    .graph-container {
      width: 100%;
      position: relative;
      background: #fdfdfd;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      overflow: hidden;
    }
    svg {
      display: block;
      width: 100%;
      height: auto;
    }
    .grid-line {
      stroke: #f1f5f9;
      stroke-width: 1;
    }
    .axis-line {
      stroke: #94a3b8;
      stroke-width: 1.5;
    }
    .asymptote-line {
      stroke: #cbd5e1;
      stroke-width: 1.5;
      stroke-dasharray: 4 3;
    }
    .axis-text {
      font-size: 10px;
      fill: #64748b;
      user-select: none;
    }
    .curve-path {
      fill: none;
      stroke: #7c3aed;
      stroke-width: 2.5;
      stroke-linecap: round;
    }
    .point-dot {
      fill: #ffffff;
      stroke: #7c3aed;
      stroke-width: 2;
      cursor: pointer;
      transition: r 0.2s, fill 0.2s;
    }
    .point-dot.active {
      fill: #7c3aed;
      stroke: #ffffff;
      stroke-width: 2.5;
      filter: drop-shadow(0 2px 4px rgba(124, 58, 237, 0.4));
    }
    .highlight-group {
      pointer-events: none;
      transition: transform 0.25s ease-out;
    }
    .coord-label {
      font-size: 11px;
      font-weight: 700;
      fill: #7c3aed;
      background: white;
    }
  </style>
</head>
<body>

  <div class="header-bar">
    <div class="func-tag">y = 8 · (½)ˣ</div>
    <div class="controls">
      <button class="btn-play" id="playBtn" onclick="togglePlay()">⏸ Pause</button>
      <button class="btn-step" onclick="prevStep()">◀</button>
      <button class="btn-step" onclick="nextStep()">▶</button>
    </div>
  </div>

  <div class="main-layout">
    
    <div class="calc-list" id="calcList">
      <div class="calc-row" onclick="goToStep(0)">
        <span class="x-val">x = -1</span>
        <span class="math-expr">8 · (0.5)⁻¹ = 8 · 2</span>
        <span class="y-res">16</span>
      </div>
      <div class="calc-row" onclick="goToStep(1)">
        <span class="x-val">x = 0</span>
        <span class="math-expr">8 · (0.5)⁰ = 8 · 1</span>
        <span class="y-res">8</span>
      </div>
      <div class="calc-row" onclick="goToStep(2)">
        <span class="x-val">x = 1</span>
        <span class="math-expr">8 · (0.5)¹ = 8 · 0.5</span>
        <span class="y-res">4</span>
      </div>
      <div class="calc-row" onclick="goToStep(3)">
        <span class="x-val">x = 2</span>
        <span class="math-expr">8 · (0.5)² = 8 · 0.25</span>
        <span class="y-res">2</span>
      </div>
      <div class="calc-row" onclick="goToStep(4)">
        <span class="x-val">x = 3</span>
        <span class="math-expr">8 · (0.5)³ = 8 · 0.125</span>
        <span class="y-res">1</span>
      </div>
    </div>

    
    <div class="graph-container">
      <svg id="graphSvg" viewBox="0 0 300 240">
        
        <g id="gridGroup"></g>
        <g id="axesGroup"></g>
        
        <path id="curve" class="curve-path" />
        
        <g id="pointsGroup"></g>
        
        <g id="activeMarker" class="highlight-group">
          <circle r="7" fill="#7c3aed" stroke="#ffffff" stroke-width="2.5" />
          <rect id="tipBg" x="8" y="-20" width="56" height="20" rx="4" fill="#7c3aed" />
          <text id="tipText" x="36" y="-6" text-anchor="middle" fill="#ffffff" font-size="11" font-weight="bold">(0, 8)</text>
        </g>
      </svg>
    </div>
  </div>

  <script>
    const data = [
      { x: -1, y: 16 },
      { x: 0, y: 8 },
      { x: 1, y: 4 },
      { x: 2, y: 2 },
      { x: 3, y: 1 }
    ];

    // Coordinate domain & range
    const xMin = -1.5, xMax = 3.8;
    const yMin = -1.2, yMax = 17.5;
    const padL = 34, padR = 16, padT = 16, padB = 26;
    const svgW = 300, svgH = 240;

    function toSvgX(x) {
      return padL + ((x - xMin) / (xMax - xMin)) * (svgW - padL - padR);
    }
    function toSvgY(y) {
      return svgH - padB - ((y - yMin) / (yMax - yMin)) * (svgH - padT - padB);
    }

    // Build Grid & Axes
    function initGraph() {
      const gridG = document.getElementById('gridGroup');
      const axesG = document.getElementById('axesGroup');

      // Horizontal grid lines & y-ticks
      for (let y = 0; y <= 16; y += 4) {
        const sy = toSvgY(y);
        gridG.innerHTML += `<line class="grid-line" x1="${padL}" y1="${sy}" x2="${svgW - padR}" y2="${sy}" />`;
        axesG.innerHTML += `<text class="axis-text" x="${padL - 6}" y="${sy + 3.5}" text-anchor="end">${y}</text>`;
      }

      // Vertical grid lines & x-ticks
      for (let x = -1; x <= 3; x += 1) {
        const sx = toSvgX(x);
        gridG.innerHTML += `<line class="grid-line" x1="${sx}" y1="${padT}" x2="${sx}" y2="${svgH - padB}" />`;
        axesG.innerHTML += `<text class="axis-text" x="${sx}" y="${svgH - padB + 14}" text-anchor="middle">${x}</text>`;
      }

      // X-Axis (y = 0)
      const zeroY = toSvgY(0);
      axesG.innerHTML += `<line class="axis-line" x1="${padL}" y1="${zeroY}" x2="${svgW - padR}" y2="${zeroY}" />`;
      // Y-Axis (x = 0)
      const zeroX = toSvgX(0);
      axesG.innerHTML += `<line class="axis-line" x1="${zeroX}" y1="${padT}" x2="${zeroX}" y2="${svgH - padB}" />`;

      // Asymptote label / line
      axesG.innerHTML += `<line class="asymptote-line" x1="${padL}" y1="${zeroY}" x2="${svgW - padR}" y2="${zeroY}" />`;
      axesG.innerHTML += `<text class="axis-text" x="${svgW - padR - 2}" y="${zeroY - 4}" text-anchor="end" fill="#94a3b8" font-size="9">y = 0 (asymptote)</text>`;

      // Sample curve dynamically: y = 8 * (0.5)^x
      let d = '';
      const step = 0.05;
      for (let x = -1.15; x <= 3.6; x += step) {
        const y = 8 * Math.pow(0.5, x);
        const sx = toSvgX(x);
        const sy = toSvgY(y);
        d += (d === '' ? 'M' : 'L') + `${sx.toFixed(1)},${sy.toFixed(1)} `;
      }
      document.getElementById('curve').setAttribute('d', d);

      // Render clickable dot nodes for key integer points
      const ptG = document.getElementById('pointsGroup');
      data.forEach((p, idx) => {
        const sx = toSvgX(p.x);
        const sy = toSvgY(p.y);
        ptG.innerHTML += `<circle id="dot-${idx}" class="point-dot" cx="${sx}" cy="${sy}" r="5" onclick="goToStep(${idx})" />`;
      });
    }

    let currentStep = 1; // Start at (0, 8)
    let isPlaying = true;
    let timer = null;

    function renderStep() {
      const rows = document.querySelectorAll('.calc-row');
      rows.forEach((r, i) => {
        r.classList.toggle('active', i === currentStep);
      });

      data.forEach((p, i) => {
        const d = document.getElementById(`dot-${i}`);
        if (d) d.classList.toggle('active', i === currentStep);
      });

      const pt = data[currentStep];
      const sx = toSvgX(pt.x);
      const sy = toSvgY(pt.y);

      const marker = document.getElementById('activeMarker');
      marker.setAttribute('transform', `translate(${sx}, ${sy})`);

      const tipBg = document.getElementById('tipBg');
      const tipText = document.getElementById('tipText');
      tipText.textContent = `(${pt.x}, ${pt.y})`;

      // Adjust popup label orientation near borders
      if (pt.x >= 2) {
        tipBg.setAttribute('x', '-64');
        tipText.setAttribute('x', '-36');
      } else {
        tipBg.setAttribute('x', '8');
        tipText.setAttribute('x', '36');
      }
    }

    function goToStep(idx) {
      currentStep = idx;
      renderStep();
    }

    function nextStep() {
      currentStep = (currentStep + 1) % data.length;
      renderStep();
    }

    function prevStep() {
      currentStep = (currentStep - 1 + data.length) % data.length;
      renderStep();
    }

    function togglePlay() {
      isPlaying = !isPlaying;
      document.getElementById('playBtn').textContent = isPlaying ? '⏸ Pause' : '▶ Play';
      if (isPlaying) {
        startTimer();
      } else {
        clearInterval(timer);
      }
    }

    function startTimer() {
      clearInterval(timer);
      timer = setInterval(() => {
        if (isPlaying) nextStep();
      }, 3200);
    }

    initGraph();
    renderStep();
    startTimer();
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #ffffff;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100vh;
      padding: 16px;
      user-select: none;
      -webkit-user-select: none;
    }

    .main-wrap {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 18px;
    }

    .instruction {
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
      letter-spacing: 0.02em;
      text-transform: uppercase;
    }

    /* Equation Display */
    .equation-box {
      display: flex;
      align-items: baseline;
      justify-content: center;
      font-family: "Cambria Math", "KaTeX_Math", "Times New Roman", serif;
      font-size: 52px;
      font-weight: 700;
      line-height: 1;
      padding: 18px 28px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 16px;
      gap: 4px;
    }

    .static-sym {
      color: #334155;
      padding: 0 2px;
    }

    .var-token {
      position: relative;
      cursor: pointer;
      padding: 4px 8px;
      border-radius: 10px;
      transition: background-color 0.2s ease, color 0.2s ease, box-shadow 0.2s ease;
      display: inline-flex;
      align-items: baseline;
    }

    .var-token.var-a {
      color: #2563eb;
    }
    .var-token.var-a.active,
    .var-token.var-a:hover {
      background: #dbeafe;
      box-shadow: 0 0 0 2px #2563eb;
    }

    .var-token.var-b {
      color: #16a34a;
    }
    .var-token.var-b.active,
    .var-token.var-b:hover {
      background: #dcfce7;
      box-shadow: 0 0 0 2px #16a34a;
    }

    .var-token.var-x {
      color: #ea580c;
      font-size: 34px;
      position: relative;
      top: -16px;
      padding: 2px 6px;
      margin-left: -2px;
    }
    .var-token.var-x.active,
    .var-token.var-x:hover {
      background: #ffedd5;
      box-shadow: 0 0 0 2px #ea580c;
    }

    /* Tab Selector for direct touch */
    .button-group {
      display: flex;
      gap: 8px;
      width: 100%;
      justify-content: center;
    }

    .select-btn {
      flex: 1;
      max-width: 110px;
      padding: 8px 12px;
      font-size: 14px;
      font-weight: 700;
      font-family: inherit;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      background: #ffffff;
      color: #64748b;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      transition: all 0.2s ease;
    }

    .select-btn .dot {
      width: 8px;
      height: 8px;
      border-radius: 50%;
    }

    .select-btn[data-target="a"] .dot { background: #2563eb; }
    .select-btn[data-target="b"] .dot { background: #16a34a; }
    .select-btn[data-target="x"] .dot { background: #ea580c; }

    .select-btn.active[data-target="a"] {
      border-color: #2563eb;
      background: #eff6ff;
      color: #1d4ed8;
    }
    .select-btn.active[data-target="b"] {
      border-color: #16a34a;
      background: #f0fdf4;
      color: #15803d;
    }
    .select-btn.active[data-target="x"] {
      border-color: #ea580c;
      background: #fff7ed;
      color: #c2410c;
    }

    /* Annotation Card */
    .info-card {
      width: 100%;
      min-height: 108px;
      padding: 16px;
      border-radius: 12px;
      border: 1px solid #e2e8f0;
      background: #ffffff;
      display: flex;
      flex-direction: column;
      justify-content: center;
      gap: 6px;
      transition: border-color 0.25s ease, background-color 0.25s ease;
    }

    .info-card.theme-a {
      border-color: #bfdbfe;
      background: #f8faff;
    }
    .info-card.theme-b {
      border-color: #bbf7d0;
      background: #f8fdf9;
    }
    .info-card.theme-x {
      border-color: #fed7aa;
      background: #fffbf7;
    }

    .info-header {
      display: flex;
      align-items: center;
      gap: 8px;
    }

    .info-badge {
      font-size: 11px;
      font-weight: 800;
      text-transform: uppercase;
      letter-spacing: 0.05em;
      padding: 2px 8px;
      border-radius: 6px;
    }

    .theme-a .info-badge { background: #2563eb; color: #ffffff; }
    .theme-b .info-badge { background: #16a34a; color: #ffffff; }
    .theme-x .info-badge { background: #ea580c; color: #ffffff; }

    .info-title {
      font-size: 16px;
      font-weight: 700;
      color: #0f172a;
    }

    .info-desc {
      font-size: 14px;
      color: #475569;
      line-height: 1.4;
    }

    .info-desc code {
      font-family: "Cambria Math", "KaTeX_Math", monospace;
      font-weight: 600;
      background: rgba(0,0,0,0.04);
      padding: 1px 4px;
      border-radius: 4px;
    }
  </style>
</head>
<body>

  <div class="main-wrap">
    <div class="instruction">Tap or hover a variable</div>

    
    <div class="equation-box" id="eqBox">
      <span class="static-sym">y</span>
      <span class="static-sym">=</span>
      <span class="var-token var-a active" data-var="a" tabindex="0" role="button" aria-label="Initial Value a">a</span>
      <span class="static-sym">·</span>
      <span class="var-token var-b" data-var="b" tabindex="0" role="button" aria-label="Base b">b</span>
      <span class="var-token var-x" data-var="x" tabindex="0" role="button" aria-label="Exponent x">x</span>
    </div>

    
    <div class="button-group">
      <button class="select-btn active" data-target="a">
        <span class="dot"></span>a
      </button>
      <button class="select-btn" data-target="b">
        <span class="dot"></span>b
      </button>
      <button class="select-btn" data-target="x">
        <span class="dot"></span>x
      </button>
    </div>

    
    <div class="info-card theme-a" id="infoCard">
      <div class="info-header">
        <span class="info-badge" id="infoBadge">Variable a</span>
        <span class="info-title" id="infoTitle">Initial Value / y-intercept</span>
      </div>
      <div class="info-desc" id="infoDesc">
        Starting amount when <code>x = 0</code>, so <code>y = a</code>.
      </div>
    </div>
  </div>

  <script>
    const data = {
      a: {
        badge: 'Variable a',
        title: 'Initial Value / y-intercept',
        desc: 'Starting amount when <code>x = 0</code>, so <code>y = a</code>.',
        theme: 'theme-a'
      },
      b: {
        badge: 'Base b',
        title: 'Base / Multiplier',
        desc: 'Growth or decay factor (must be <code>> 0</code> and <code>≠ 1</code>).',
        theme: 'theme-b'
      },
      x: {
        badge: 'Exponent x',
        title: 'Exponent / Input',
        desc: 'Number of steps, intervals, or elapsed time.',
        theme: 'theme-x'
      }
    };

    const tokens = document.querySelectorAll('.var-token');
    const buttons = document.querySelectorAll('.select-btn');
    const infoCard = document.getElementById('infoCard');
    const infoBadge = document.getElementById('infoBadge');
    const infoTitle = document.getElementById('infoTitle');
    const infoDesc = document.getElementById('infoDesc');

    let currentVar = 'a';

    function setVariable(key) {
      if (!data[key]) return;
      currentVar = key;

      tokens.forEach(t => {
        t.classList.toggle('active', t.getAttribute('data-var') === key);
      });

      buttons.forEach(b => {
        b.classList.toggle('active', b.getAttribute('data-target') === key);
      });

      infoCard.className = 'info-card ' + data[key].theme;
      infoBadge.textContent = data[key].badge;
      infoTitle.textContent = data[key].title;
      infoDesc.innerHTML = data[key].desc;
    }

    tokens.forEach(token => {
      const key = token.getAttribute('data-var');
      token.addEventListener('mouseenter', () => setVariable(key));
      token.addEventListener('click', () => setVariable(key));
      token.addEventListener('keydown', (e) => {
        if (e.key === 'Enter' || e.key === ' ') {
          e.preventDefault();
          setVariable(key);
        }
      });
    });

    buttons.forEach(btn => {
      const key = btn.getAttribute('data-target');
      btn.addEventListener('click', () => setVariable(key));
      btn.addEventListener('mouseenter', () => setVariable(key));
    });
  </script>
</body>
</html>

HSN.Q.A.2

Aligned learning resources

Related diagrams