|
Server : Apache/2.4.62 System : FreeBSD fbsdweb2.web.rcn.net 14.1-RELEASE FreeBSD 14.1-RELEASE releng/14.1-n267679-10e31f0946d8 GENERIC amd64 User : www ( 80) PHP Version : 8.3.8 Disable Function : NONE Directory : /domains/drsuper/CalculusMechanics/ |
Upload File : |
<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8" />
<title>Adventure 9 — Exponential Decay & the Age of the Earth</title>
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<style>
body {
font-size: 18px;
font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", sans-serif;
margin: 0;
padding: 0;
background: #f5f5fb;
color: #222;
}
.wrap{
padding: 12px 18px;
max-width: 1600px;
margin: 0 auto;
}
.page {
width: 100%;
box-sizing: border-box;
padding: 1.8rem 5vw 3rem;
background: #ffffff;
max-width: 1250px;
margin: 0 auto;
}
h1 { margin: 0.2rem 0 0.25rem; font-size: 2.1rem; }
.subtitle { color: #555; margin: 0 0 1.2rem; line-height: 1.45; }
h2 { margin-top: 1.4rem; margin-bottom: 0.4rem; font-size: 1.55rem; }
p { margin: 0.35rem 0 0.7rem; line-height: 1.55; }
ul { margin-top: 0.3rem; padding-left: 1.2rem; }
li { margin: 0.25rem 0; }
a { color: #1f4ed8; text-decoration: none; }
a:hover { text-decoration: underline; }
.toplinks { font-size: 0.95rem; margin-bottom: 0.8rem; }
.card {
border: 1px solid #dde3ff;
background: #f6f7ff;
border-radius: 14px;
padding: 1rem 1rem 0.95rem;
margin-top: 0.7rem;
}
.callout {
background: #f3f6ff;
border-radius: 10px;
border: 1px solid #dde3ff;
padding: 0.9rem 1rem;
font-size: 0.98rem;
margin: 1rem 0;
}
.questions {
background: #fff9e5;
border-radius: 10px;
border: 1px solid #f0e0a0;
padding: 0.9rem 1rem;
font-size: 0.98rem;
margin: 1rem 0;
}
.blank{display:none;}
.blank.sm { min-width: 120px; }
.blank.lg { min-width: 360px; }
code { background:#fff; border:1px solid #d9def5; padding:2px 6px; border-radius:8px; }
.footer {
margin-top: 2.2rem;
font-size: 0.9rem;
color: #777;
text-align: left;
border-top: 1px solid #eee;
padding-top: 0.8rem;
}
/* --- Adventure 4 two-column layout (questions left, chart right) --- */
.page { max-width: none !important; } /* full width */
.two-col {
display: grid;
grid-template-columns: 1.45fr 0.55fr;
gap: 2rem;
align-items: start;
clear: both;
}
.right-col { text-align: center; }
.chart-sticky {
position: sticky;
top: 1rem;
}
@media (max-width: 900px) {
.two-col { grid-template-columns: 1.45fr 0.55fr; }
.chart-sticky { position: static; }
}
/* --- Interactive answer inputs (Adventure style) --- */
input[type="text"], input[type="number"]{
width: 100%;
max-width: 260px;
padding: 0.35rem 0.45rem;
font-size: 18px;
border-radius: 8px;
border: 1px solid #c3cade;
margin-top: 0.25rem;
box-sizing: border-box;
}
textarea{
width: 100%;
max-width: 520px;
padding: 0.45rem 0.55rem;
font-size: 0.95rem;
border-radius: 10px;
border: 1px solid #c3cade;
margin-top: 0.25rem;
box-sizing: border-box;
line-height: 1.45;
}
.row-grid {
display: grid;
grid-template-columns: repeat(2, minmax(0, 1fr));
gap: 1rem 1.6rem;
margin-top: 0.6rem;
clear: both;
}
button {
background: #e9f0ff;
border: 2px solid #6b8cff;
border-radius: 0;
padding: 10px 18px;
font-size: 1rem;
cursor: pointer;
box-shadow: 0 3px 0 #4f6fe6;
transition: all 0.12s ease;
}
/* Hover */
button:hover {
background: #f3f7ff;
}
/* Pressed */
button:active {
background: #cddcff;
box-shadow: 0 1px 0 #4f6fe6;
transform: translateY(2px);
}
/* Optional: "checked" feeling after click */
button.checked {
background: #dff5e1;
border-color: #3a9b3a;
box-shadow: inset 0 2px 4px rgba(0,0,0,0.15);
}
button.sampled {
background: #fff3d9;
border-color: #d9a441;
box-shadow: inset 0 2px 4px rgba(0,0,0,0.15);
}
.correct {
background-color: #e4f9e7 !important;
border-color: #2e9a48 !important;
}
.incorrect {
background-color: #fde3e3 !important;
border-color: #cc3d3d !important;
}
.hint, .solution {
margin-top: 0.9rem;
padding: 0.8rem 0.9rem;
border-radius: 10px;
border: 1px solid #dde3ff;
background: #f6f7ff;
font-size: 0.92rem;
display: none;
}
@media (max-width: 900px) {
.row-grid { grid-template-columns: 1fr; }
}
.right-col{position:sticky; top:1rem; align-self:start;}
/* === DiVA chart sizing (best fit) === */
.chart-box{
height: 540px; /* best-fit: tall enough for readability, keeps 2-column balance */
border-radius: 12px;
border: 1px solid #dde3ff;
background: #ffffff;
display: flex;
align-items: center;
justify-content: center;
margin-bottom: 16px;
box-shadow: 0 6px 18px rgba(0,0,0,0.12);
padding: 10px;
box-sizing: border-box;
}
.chart-box img{width:90%;height:auto;display:block;border-radius:10px;margin:0 auto}</style>
</head>
<body>
<div class="page">
<div class="wrap">
<div style="display:flex; flex-wrap:wrap; gap:12px; margin-bottom:0.8rem;">
<a href="index.html"><button>🧭 Hub</button></a>
<a href="adventure_9_story.html"><button class="secondary">📜 Story</button></a>
<a href="adventure_9.html"><button class="secondary">✅ Activity</button></a>
</div>
</div>
<h1>🌍 Adventure 9 — Exponential Decay & the Age of the Earth</h1>
<div class="subtitle">Using U‑235, half‑life, and a DiVA chart to estimate Earth’s age — and meet Clair Patterson.</div>
<h2>🎯 What you will learn</h2>
<div class="callout"><ul>
<li>Radioactive decay follows an <b>exponential</b> law.</li>
<li><b>Half‑life</b> acts like a built‑in clock (powers of 2).</li>
<li><b>v(t)</b> is the <b>decay speed</b> (how fast uranium turns into lead).</li>
<li><b>Area under v(t)</b> tells how much mass has changed.</li>
</ul></div>
<h2>🎥 Watch: Why exponential growth and decay are special</h2>
<div class="callout">
<ul>
<li>
🎥 <strong>
<a href="https://www.youtube.com/watch?v=m2MIpDrF7Es&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr&index=5"
target="_blank" rel="noopener">
What's so special about Euler’s number e?
<br>
<span style="font-weight:normal;">3Blue1Brown — Essence of Calculus, Chapter 5</span>
</a></strong>
<p>This mysterious number appears again and again in nature, linking growth, decay, and time itself.</p>
</li>
</ul>
</div>
<h2>📖 1) Read / Listen: Story</h2>
<div class="callout">
<ul><li>📖 <strong><a href="adventure_9_story.html">“The Age of Earth — Clair Patterson & the Planet Covered in Lead”</a></strong></li></ul>
<li>Watch exponential change reveal patterns that stretch from tiny scales to billions of years.</li>
</div>
<h2>✏️ 2) Do the Adventure Activity</h2>
<div class="callout">
<ul><li>✏️ <strong><a href="adventure_9.html">Open: Adventure 9 — Activity Page</a></strong></li></ul>
<li>Use the DiVA chart to estimate Earth’s age from uranium decay — and see how it matches Clair’s discovery.</li>
</div>
<div class="callout">
<h2>📈 3) Charts</h2>
<ul><li>📈 <strong><a href="adventure_9_charts.pdf" target="_blank" rel="noopener">Open: Adventure 9 — Charts (PDF)</a></strong></li></ul>
</div>
<div class="footer">Dr. Super & Spark — Powered by ChatGPT</div>
</div></body></html>