Evaluating an Exponential Decay Function
Plutonium, a radioactive material used in most nuclear reactors, decays exponentially at a rate of 0.003% per year. If there are originally 2000 grams of plutonium, the amount of plutonium, P, remaining after t years is P(t) = 2000e^{-0.00003t}. How much plutonium will remain after 50 years?
Substitute 50 years for t in the function, then evaluate using a calculator as described earlier.
P(t) = 2000e^{-0.00003t}
P(50) = 2000e^{-0.00003(50)}
= 2000e^{-0.0015}
≈ 2000(0.9985011244)
≈ 1997.0 grams
Thus, after 50 years, the amount of plutonium remaining will be about 1997 grams.