The half-life of a radioactive substance is the time it takes to decay by
one-half. The half-life of carbon 14, which is used for dating previously
living things, is 5500 years. When an organism dies, it stops accumulating
carbon 14. The carbon 14 present at the time of death decays with time.
Let C(t)/C(0) be the fraction of carbon 14 remaining at time t. In
radioactive carbon dating, scientists usually assume that the remaining
fraction decays exponentially according to the following formula:
C(t)C(0)=e−bt

a. Use the half-life of carbon 14 to nd the value of the parameter b, and
plot the function.
b. If 90 percent of the original carbon 14 remains, estimate how long ago
the organism died.
c. Suppose our estimate of b is off by ±1 percent. How does this error
affect the age estimate?