Radioactive decay. Carbon-14 has a decay rate of 0.012097% per year. The rate of change of an amount N of carbon-14 is given by where t is the number of years since decay began.

a) Let N0 represent the amount of carbon-14 present at t = 0. Find the exponential function that models the situation.

b) Suppose 200 g of carbon-14 is present at t = 0. How much will remain after 800 yr?

c) After how many years will half of the 200 g of carbon-14 remain?