Question

An element with mass 310 grams decay by 5. 7% per minute. How much of the element is remaining after 9 minutes, to the nearest 10th of a gram

Answer 1

`\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &310\\ r=rate\to 5.7\%\to (5.7)/(100)\dotfill &0.057\\ t=minutes\dotfill &9\\ \end{cases} \\\\\\ A = 310(1 - 0.057)^(9)\implies A=310(0.943)^9 \implies A \approx 182.8`

Answer 2

It will be 182.8 g.

Explanation:

So, at the end of the first minute, you will have .943 x 310 = 292.33 gAt the end of the second minute, you will have .943 x 292.33 = .943 x (.943 x 310) = 275.67At the end of the third minute, you will have .943 x 275.67 = .943 x .943 x (.943 x 310) = 259.95 gNow you can see the trend, at the end of n minutes, there is (.943)n x 310 gramsSo, after 9 minutes, the amount of material remaining is (.943)9 x 310 = 182.8 grams