Answer to Question #344697 in Algebra for ALE

Question

An element with mass 140 grams decays by 21.6% per minute. How much of the element is remaining after 20 minutes, to the nearest 10th of a gram?

Answer 1

Exponential equation of decay : 

y=A(1−r)^x

  where, A = initial value , r= rate of decay in decimal , x= time.

As per given : Initial mass : A= 140 grams

Rate of decay : r= 21.6% per minute= 0.216 per minute.

x= 20 minutes

Substitute values in (i) , we get

$\begin{gathered}y=140(1-0.216)^{20}\\\\=140(0.784)^{20}=1.0775794222\approx1.1\text{ gram}\end{gathered}$

Hence, the mass of the remaining element = 1.1 grams .

ANSWER: The mass of the remaining element = 1.1 grams .