Chapter 1.1, Problem 7P

A radioactive material, such as the isotope thorium $-234$, disintegrates at a rate proportional to the amount currently present. If $Q(t)$ is the amountat time $t$, then $dQ/dt=-rQ$, where $r>0$ is the decay rate.

If $100$ milligrams (mg) of thorium $-234$ decays to $82.04$ mg in $1$ week, determine the decay rate $r$.

Find an expression for the amount of thorium $-234$ present at any time $t$.

Find the time required for the thorium $-234$ to decay toone-half its original amount.