Question

Plutonium-240 decays according to the function 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. 1.44 years B. 18,900 years C. 9,990 years D. 2,100 years

Answer 1

according to the function ...
let me guess,
\[A(t)=A_0e^{-kt}\]

Answer 2

well yes but the varible is actually Q but that dosent really matter, i just cant get the answer i dont know how to do it

Answer 3

first replace \(k \) by \(-0.00011\) and \(Q_0\) by \(36\) to get
\[\large Q(t)=36e^{-0.00011t}\]

Answer 4

set that sucker equal to \(12\) and solve \[\large Q(t)=36e^{-0.00011t}=12\] in only three steps

Answer 5

1) divide by 36
2) rewrite in logarithmic form
3) divide by \(-0.00011\)

Answer 6

let me know if that is clear

Answer 7

thanks for your help i got 9987.38 is that correct? would the answer be C?

Answer 8

i have no idea, i didn't do it, but i would be happy to check the answer

Answer 9

please do i want to see if ive done it correctly

Answer 10

that is what i get too
in any case the answer is almost always C, so you could have done this without doing any work at all

Answer 11

haha thanks

Answer 12

yw