(a) Show that if the decay rate is R₀ at time t = 0 and R₁ at some later time t₁, the decay constant is given by λ = t₁^-1 ln(R₀/R₁) and the half-life is given by t_1/2 = 0.693t₁/ln(R₀/R₁).

(b) Use these results to find the decay constant and the half-life if the decay rate is 1200 Bq at t = 0 and 800 Bq at t₁ = 60 s.