Homework Help: calculus

Posted by zak on Thursday, February 26, 2009 at 11:21pm.

Question: "Plutonium isotope Pu-239 has a half-life of 24,100 years. Suppose that 10 grams of Pu-239 was released in the Chernobyl nuclear accident. How long will it take for the 10 grams to decay to 1 gram?"

I know that I am suppose to use
y= ye^kt , to get the equation and then plug in the info. to get the time, but I'm not sure how to start, please help! Thanks!

calculus - Reiny, Thursday, February 26, 2009 at 11:55pm
y = a e^(kt) where a is the initial amount
so y = 10(e^(kt))
when t = 24100, y = 5 ---> you should have 1/2 of the original 10 g left.

0.5 = e^(24100k)
24100k = ln(0.5)
k = ln(.5)/24100
so y = 10(e^(t)(ln.5/24100))
so you want y to be 1

1 = 10 (e^(t)(ln.5/24100))
0.1 = (e^(t)(ln.5/24100))

(t)(ln.5/24100)) = ln .1
t = 80059

so about 80,000 years !!!!
calculus - zak, Friday, February 27, 2009 at 3:06am
Ohhh, I get it!! Thanks so much, you helped me a lot! :)

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