Question 6.10.10: Evaluating an Exponential Decay Function Plutonium, a radioa......

A Survey of Mathematics with Applications [1175400]

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?

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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.

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