Plutonium-238 has a yearly decay constant of 7.9 * 10-3. If an original sample has a mass of 15 grams, how long will it take to decay to 12 grams?

(At = A0e-kt)

The answer is 28 years

At = A0 * e^ (-k * t)

At = 12 g

A0 = 15 g

k = 7.9 * 10^-3 = 0.0079

t = ?

12 = 15 * e^ (-0.0079 * t)

12/15 = e^ (-0.0079 * t)

0.8 = e^ (-0.0079 * t)

Logarithm both sides (because ln (e) = 1:

ln (0.8) = ln (e^ (-0.0079 * t))

ln (0.8) = (-0.0079 * t) * ln (e)

-0.223 = - 0.0079 * t

t = - 0.223 / - 0.0079

t = 28.23

t ≈ 28 years