Question: (a) Consider the initial-value problem dA/dt = kA, A(0) = A 0 as the model for the decay of a radioactive substance. Showthat, in general,

(a) Consider the initial-value problem dA/dt = kA, A(0) = A₀ as the model for the decay of a radioactive substance. Showthat, in general, the half-life T of the substance is T = 2(ln 2)/k.

(b) Show that the solution of the initial-value problem in part (a) can be written A(t) = A₀2^-t/T.

(c) If a radioactive substance has the half-life T given in part (a), how long will it take an initial amount A₀ of the substance to decay to 1/8 A₀?

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