Question

If 10 g of a radioactive substance are present initially and 2 yr later only 5.0 g​ remain, how much of the​ substance, to the nearest tenth of a​ gram, will be present after 5 ​yr?

Answer 1

1.8 grams

Explanation:

You want to know how much of 10 g of a substance remains after 5 years, if it has a half-life of 2 years.

Exponential decay

The amount remaining can be modeled by the exponential decay function ...

a(t) = 10·(1/2)^(t/2)

The exponent t/2 tells how many half-lives have passed, and the factor (1/2)^(t/2) cuts the amount remaining in half for each of them.

Application

Using t=5, we find the amount remaining to be ...

a(5) = 10·(1/2)^(5/2) ≈ 1.8 . . . . grams

About 1.8 grams of the substance will be present after 5 years.