Chapter 1.1, Problem 6P

Radioactive Decay. Experiments show that a radioisotope decays at a rate negatively proportional to the amount of the isotope present.

Use the following variables and parameters to writedown and solve an initial value problem for the process ofradioactive decay: $t=$ time; $a(t)=$ amount of the radioisotope present at time $t$; $a_0=$ initial amount of radioisotope; $r=$ decay rate, where $r>0$.

The half-life, $T_{1/2}$, of a radioisotope is the amount oftime it takes for a quantity of the radioactive material to decay to one-half of its original amount. Find an expression for $T_{1/2}$ in terms of the decay rate $r$.