Plutonium-240 decays according to the function $$Q(t)=Q _{o}e ^{-kt}$$ where Q represents the quantity remaining after t years and k is the decay constant, 0.00011... How long will it take 36 grams of plutonium-240 to decay to 12 grams?

A. 18,900 years
B. 1.44 years
C. 9,990 years
D. 2,100 years

Question

Plutonium-240 decays according to the function $$Q(t)=Q _{o}e ^{-kt}$$ where Q represents the quantity remaining after t years and k is the decay constant, 0.00011... How long will it take 36 grams of plutonium-240 to decay to 12 grams?

A. 18,900 years
B. 1.44 years
C. 9,990 years
D. 2,100 years

anonymous · Answer

so Qt = 12
Qo=36

anonymous · Answer

use the rule of logarithms.  take natural log of both sides

anonymous · Answer

how exactly do i do that? like what would the equation look like?

anonymous · Answer

right now the equation is:

12=36*e^(-0.00011*t)

anonymous · Answer

so if you take the natural log of both sides, you get

anonymous · Answer

ln(12/36)=ln(e^0.00011*t)

anonymous · Answer

and ln(e^x) = x

anonymous · Answer

so you get

ln(12/36)=0.00011*t

anonymous · Answer

so t = ln(12/36) / 0.00011

anonymous · Answer

make sense?

anonymous · Answer

well that makes sense, but for the answer i got no solution, what are your thoughts?

anonymous · Answer

the answer should be C per the equation i gave

anonymous · Answer

also k is negative

anonymous · Answer

hm, I'll double check my work, thank you :)

anonymous · Answer

if it decays, then k is negative

anonymous · Answer

Answer should be a