Answer to Question #287711 in Algebra for Lil

Question #287711

An element with mass 780 grams decays by 16.3% per minute. How much of the element is remaining after 16 minutes, to the nearest 10th of a gram?


1
Expert's answer
2022-01-17T18:47:10-0500

The remaining mass of the element decays by 16.3%: initially, we have 780 g, after the first minute we have 780·(1-0.163)=652.9 g, then (by the end of the second minute) we have 652.9(1-16.3)=780·(1-0.163)2, later we have 780·(1-0.163)3, and so on. Therefore, the rule is


m=780(10.163)t.m=780(1-0.163)^t.

After 16 minutes the remaining mass is:


m=780(10.163)16=45.3 g.m=780(1-0.163)^{16}=45.3\text{ g}.


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