Posted by zak on Thursday, February 26, 2009 at 11:21pm.
Question: "Plutonium isotope Pu239 has a halflife of 24,100 years. Suppose that 10 grams of Pu239 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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