Question

An element with mass 730 grams decays by 28.8% per minute. How much of the element is remaining after 10 minutes, to the nearest 10th of a gram?

Answer 1

Answer:

A= 24.4 grams

Step-by-step explanation:

An element with mass 730 grams decays by 28.8% per minute

For exponential decay we use formula

$A= P(1-r)^t$

Where P is the initial amount of element present

A is the amount remaining

r is the decay rate

and t is the time period in minutes

P= 730 grams, r= 28.8%= 28.8/100= 0.288, t= 10 minutes

$A= 730(1-0.288)^10$

A=24.44122

Round to nearest tenth

So A= 24.4 grams

Answer 2

$\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &730\\ r=rate\to 28.8\%\to \frac{28.8}{100}\to &0.288\\ t=\textit{elapsed time}\to &10\\ \end{cases} \\\\\\ A=730(1-0.288)^{10}\implies A=730(0.712)^{10}$