The half-life of a radioactive substance is the time it takes to decay by 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, it is usually assumed that the remaining fraction decays exponentially according to the formula
C(t)/C(0) = e-bt
a. Use the half-life of carbon-14 to find the value of the parameter b and plot the function.
b. Suppose we estimate that 90% of the original carbon-14 remains. Estimate how long ago the organism died.
c. Suppose our estimate of h is off by ± 1 %. How does this affect the age estimate in part (b)?