Answer to Question #287711 in Algebra for Lil

Question

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?

Answer 1

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

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

After 16 minutes the remaining mass is:

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