calculus
posted by zak on .
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!

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 !!!! 
Ohhh, I get it!! Thanks so much, you helped me a lot! :)