# calculus

posted by .

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 -

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

• calculus -

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

## Similar Questions

1. ### science

suppose you have 100grams of radioactive plutonium-239 with a half-life of 24,000 years. how many grams of plutonium-239 will remain after: A)12,000 years B)24,000 years C)96,000 years how do i do this?
2. ### CHEM

Pu-239 has a half-life of 24110 y. If 1.00 kg of this isotope is present in the used fuel rods of a nuclear power plant approximately how long will it take for this amount of Pu-239 to decay until there is less than 1 mg left ?
3. ### Physics

Suppose you have 100 g of radioactive plutonium-239 with a half-life of 24,000 years. How many grams will remain after (a) 12,000 years (b) 24,000 years (c) 96,000 years?
4. ### Physics

Suppose you have 100 g of radioactive plutonium-239 with a half-life of 24,000 years. How many grams will remain after (a) 12,000 years (b) 24,000 years (c) 96,000 years?
5. ### CHEMISTRY

Suppose you had a detection device that could count every decay event from a radioactive sample of plutonium-239.052156 (t1/2 is 24,000 yr). How many counts per second would you obtain from a sample containing 0.126 g of plutonium-239?
6. ### Math

_The_Natural_Base_e_ An accident in 1986 at the Chernobyl nuculear plant in the Ukraine released a large amount of plutonium (Pu-239)into the atmosphere. The half-life of Pu-239 is about 24,110 years. Find the decay constant. Use the …
7. ### Precalcus

Suppose that 10 grams of carbon ( 14C )is released in a nuclear energy plant accident. How long will it take for the 10 gramto decay to 1 gram?
8. ### physics

The half-life of the plutonium isotope is 24,360 years. If 10 grams of plotonium is released into the atmosphere by a nuclear accident, how many years will it take for 80% of the isotope to decay?
9. ### Chemistry

If the half life of Pu-239 is 2.4 x 10^4 years, how many years are required for a 20-gram sample of plutonium-239 to be reduced to a mass of 5 grams?
10. ### Math

Plutonium-239 has a half-life of 24 000 years. What percent of plutonium-239 remains after 10 000 years?

More Similar Questions