The function Q (t) = Q (base o) e^ (-kt) maybe be used to model radioactive decay. Q represents the quantity remaining after t years; k is the decay constant, 0.00011. How long in years will it take for a quantity of plutonium-240 to decay to 25% of its original amount?

Question

Brayan

Mathematics

4 August, 07:32

The function Q (t) = Q (base o) e^ (-kt) maybe be used to model radioactive decay. Q represents the quantity remaining after t years; k is the decay constant, 0.00011. How long in years will it take for a quantity of plutonium-240 to decay to 25% of its original amount?

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Kathy English · Answer 1

Half-Life = ln (.5) / k

Half-Life =.693147 /.00011

Half-Life = 6,301 years

For a radioactive substance to decay to 25%, it has to go through 2 halflives.

2 * 6,301 = 12,602 years

approximately 12,600 years