Answer to Question #344697 in Algebra for ALE

Question #344697

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?


1
Expert's answer
2022-05-25T16:57:56-0400

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 .

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