If 40 milligrams of strontium-90 radioactively decays to 12 milligrams in 30 years, find its half-life (the number of years it takes until half of it remains). Use the formula A = p ⋅ e−kt, where p is the amount and A the (smaller) final amount.

Question

If 40 milligrams of strontium-90 radioactively decays to 12 milligrams in 30 years, find its half-life (the number of years it takes until half of it remains). Use the formula A = p ⋅ e−kt, where p is the amount and A the (smaller) final amount.

Damon · Answer

12 = 40 e^(-kt) .3 = e^-30 k ln .3 = -30 k -1.20 = -30 k k = .04013 so .5 = e^-.04013 t -.6931 = -.04013 t t = 17.3 years