Plutonium is a radioactive atom, which decays at a rate of r=(9.2)⋅10−13. Let p(t) denote the radioactivity at time t ( t is in seconds) and p0 the initial radioactivity. Then p(t) satisfies the decay equation p(t)=p0e−rt.

a) (6 pts) Find the inverse of this function and explain its meaning.

b) (4 pts) How many years does it take for a piece of plutonium of initial radioactivity of p0=100 to decay to 5% of its initial radioactivity?