<p>The mass, $M$ grams, of a radioactive substance, present at time $t$ years after first being observed, is given by the formula $M=200e^{-kt}$, where $k$ is a constant.</p>
<p>The mass of the substance was $123.7$g after being observed for $2$ years.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text"></span></div><ol class="i-list"><li><div class="list-item-paragraph">State the initial mass of the substance.<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Show that $k$ is approximately $0.240$, correct to $3$ significant figures.<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Find the mass of the substance when $t=5$,<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Find the value of $t$ when the mass of the substance is $15$% of its initial mass.</div><div class="list-item-paragraph">Give your answers correct to three significant figures.<span class="inline-marks">[2]</span></div></li></ol></li><li><div class="list-item-paragraph">Explain, with clear working, why the mass of the substance can never be more than $200$ grams<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Sketch the graph of $M$ against $t$.<span class="inline-marks">[2]</span></div></li></ol>

The mass, $M$ grams, of a radioactive substance, present at time $t$ years after first being observed, is given by the formula $M=200e^{-kt}$, where $k$ is a constant.

The mass of the substance was $123.7$g after being observed for $2$ years.

Explain, with clear working, why the mass of the substance can never be more than $200$ grams

Exponential and Logarithmic Functions - Applications of Exponential and Logarithmic Functions

Exponential and Logarithmic Functions - Applications of Exponential and Logarithmic Functions