\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} 
A radioactive substance $A$ decays at a rate proportional to
the amount of the substance present.

\medskip

\noindent a) Suppose that an initial amount of 10 micrograms decays
after 8 hours to 7 micrograms. Determine a formula for $A(t)$, the
amount of substance $A$ present at time $t$.

\medskip

\noindent b) In the presence of a certain gamma ray flux, the
radioactive decay of the substance is increased. In fact, when an
initial amount of 10 micrograms of $A$ is subject to this radiation,
after 8 hours only 2 micrograms of $A$ remain. Determine a formula for
$B(t)$, the amount of substance $A$ present at time $t$ when the
radiation mentioned is present.

\medskip

\noindent c) Suppose we are presented with 10 micrograms of substance
$A$ and wish to have 5 micrograms after 8 hours. We are allowed to
``turn on'' the gamma radiation at some time during the 8 hours (but
it must stay on after it is turned on!). At what time should the
radiation be introduced in order to obtain 5 micrograms of $A$ after 8
hours?

\vfil\eject\end