Question

The plutonium isotope Pu-239 is a radioactive material. The half-life of plutonium isotope Pu-239 is 24, 360 years. If 10 grams of plutonium were released in nuclear accident, how long will it take for the 10 gram to decay to 1 gram? Round off your answer to the nearest year

Answer 1

i could have sworn i just answered this question
maybe it was not clear

Answer 2

half live is 360 years, so we can model it as \(A_0(\frac{1}{2})^{\frac{t}{360}}\)
in your case you start with 10, so it is
\[10(\frac{1}{2})^{\frac{t}{360}}\] and you want to know when this is equal to 1, so set
\[1=10(\frac{1}{2})^{\frac{t}{360}}\] and solve for \(t\)

Answer 3

step one, divide by 10 to get
\[.1=(\frac{1}{2})^{\frac{t}{360}}\]

Answer 4

I think that is 24,360 years.

Answer 5

step 2
use the change of base formula
\(A=b^x\iff x=\frac{\ln(b)}{\ln(A)}\)
to get
\[\frac{t}{360}=\frac{\ln(.1)}{\ln(.5)}\]

Answer 6

step 3 is to multiply both sides by 360 and get
\[t=\frac{360\ln(.1)}{\ln(.5)}\]

Answer 7

step for is calculator
http://www.wolframalpha.com/input/?i=360ln%28.1%29%2Fln%28.5%29

Answer 8

*four

Answer 9

\[t=\frac{24,360 \ln (.1)}{\ln (.5)}\]

Answer 10

I was taught to use e when doing this, but I like your method. The OP put a space in their half-life which made it hard to read. I looked it up and PU-239 usually has a half-life around 24k years... so I think they meant 24,360. But your method is smooth.