<p>The mass, \(m\) mg, of a radioactive substance decreases with time, \(t\) hours.</p>
<p>It is known that&nbsp;\(m\) and \(t\) are related by the equation \(m = Me^{-kt}\), where&nbsp;\(M\) and \(k\) are constants.</p>
<p>The table below shows measured values of \(m\) and \(t\).</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: left; --cell-justify: flex-start">\(t\) (hours)</th><th style="text-align: left; --cell-justify: flex-start">\(1\)</th><th style="text-align: left; --cell-justify: flex-start">\(2\)</th><th style="text-align: left; --cell-justify: flex-start">\(3\)</th><th style="text-align: left; --cell-justify: flex-start">\(4\)</th><th style="text-align: left; --cell-justify: flex-start">\(5\)</th></tr></thead><tbody><tr><td style="text-align: left; --cell-justify: flex-start">\(m\) (mg)</td><td style="text-align: left; --cell-justify: flex-start">\(6.55\)</td><td style="text-align: left; --cell-justify: flex-start">\(5.36\)</td><td style="text-align: left; --cell-justify: flex-start">\(4.40\)</td><td style="text-align: left; --cell-justify: flex-start">\(3.60\)</td><td style="text-align: left; --cell-justify: flex-start">\(2.94\)</td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-paragraph">Plot \(\ln m\) against \(t\) and draw a straight line graph.<span class="inline-marks">[2]</span></div><div class="list-item-paragraph">Use your graph to estimate</div></li><li><div class="list-item-paragraph">the initial mass of the substance<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">the value of k <span class="inline-marks">[2]</span></div></li></ol>

The mass, \(m\) mg, of a radioactive substance decreases with time, \(t\) hours.

It is known that \(m\) and \(t\) are related by the equation \(m = Me^{-kt}\), where \(M\) and \(k\) are constants.

2025 DSS PRELIMS P1 Q13

2025 DSS PRELIMS P1 Q13