The function Q (t) = Qe^-kt may 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 it's original amount?

Question

Alyson Hayes

Mathematics

16 February, 07:11

The function Q (t) = Qe^-kt may 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 it's original amount?

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Answers (1)

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Benton · Answer 1

It will take 12602.68 years.

Solution:

Q (t) = Qe^-kt

Q (t) = 0.25Q

0.25Q=Qe^-0.00011t

ln 0.25=-0.00011t

t = (ln 0.25) / - 0.00011 = 12602.67601