Consider the initial value problem
dA/dt = kA, A(0) = A_0 (where '_' means subscript)
as the model for the decay of a radioactive substance.

(i) Show that, in general, the half-life T of the substance is
T = - ln 2 / k.
(ii) Show that the solution of the initial value problem in part (1) can be written as
A(t) = A_(0) * 2^(e*(-t / T)).
(iii) If a radioactive substance has the half-life T given in part (i), how long will it take an initial amount A_0 of the substance to decay to 1/8 A_0?

I am at a loss as to what to do for all parts of this question. If someone who knew how to do this, would maybe express their ideas (even solve the problem!!) - well that would be wonderful!!

Thank-you!

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