Question

An element with mass 730 grams decays by 27.6% per minute. How much of the element is remaining after 12 minutes, to the nearest 10th of a gram?

Answer 1

$\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=I(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &730\\ r=rate\to 27.6\%\to \frac{27.6}{100}\to &0.276\\ t=\textit{elapsed time}\to &12\\ \end{cases} \\\\\\ A=730(1-0.276)^{12}\implies A=730(0.724)^{12}$

Answer 2

Answer: 15.1 gram

Step-by-step explanation:

The exponential decay equation with rate of decay r in time period t is given by :-

$f(x)=A(1-r)^t$, A is the initial value .

Given: The initial mass of element=  730 grams

Rate of decay= 27.6%=0.276

Thus, the function represents the amount of element after t minutes is given by ;-

$f(x)=730(1-0.276)^x\\\\\Rightarrow\ f(x)=730(0.724)^x$

Now, the function represents the amount of element after 12 minutes is given by ;-

$f(x)=730(0.724)^{12}\\\\\Rightarrow\ f(x)=15.1420841187\approx15.1\text{ grams}$

Hence, 15.1 grams of element remains after 12 minutes.