Question

If 80 mg of a radioactive element decays to 10 mg in 30 minutes, what is the element's half life in minutes?

Answer 1

Let the half-life be T minutes. Exponential decay gives
10 = 80*(1/2)^{30/T}.
So (1/2)^{30/T} = 1/8 = (1/2)^3, hence 30/T = 3 and T = 10 minutes.