Question

Plutonium-240 decays according to the function Q(t) = Qoe^-kt

where Q
represents the quantity remaining after t years and k is the decay constant,
0.00011... To the nearest 10 years, how long will it take 36 grams of
plutonium-240 to decay to 12 grams?

Answer 1

9990 years

Explanation:

The exponential function with given values filled in can be solved for the unknown using logarithms.

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Q(t) = 12 = 36e^(-0.00011t)

1/3 = e^(-0.00011t) . . . . . . divide by 36

ln(1/3) = -0.00011t . . . . . . take natural logs

t = ln(1/3)/(-0.00011) . . . . divide by the coefficient of t

t ≈ 9990 . . . years