A radioactive sample decays at a rate proportional to the amount present. It has 800 g now and a half-life of 5 years. How much is left after 15 years, in grams?

Explanation

1. 01

   $\frac{dN}{dt} = -kN$ gives $N = N_0e^{-kt}$, and each half-life halves what is left.

2. 02

   15 years is 3 half-lives: $800 \times \left(\frac{1}{2}\right)^3 = 100$ g.