SOLUTION: The radioactive element americium-241 has half the life of 432 years. Suppose we start with a 45-g mass of americium-241, how much would be left after 343 years?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The radioactive element americium-241 has half the life of 432 years. Suppose we start with a 45-g mass of americium-241, how much would be left after 343 years?      Log On


   

Question 378561: The radioactive element americium-241 has half the life of 432 years. Suppose we start with a 45-g mass of americium-241, how much would be left after 343 years?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for determining the amount of substance left is A+=+Ce%5E%28kt%29, where C is the initial amount, k is the decay constant, and t is time. We must solve for k:
Given the half-life of 432 years, we may plug in t:
C%2F2+=+Ce%5E%28432k%29
1%2F2+=+e%5E%28432k%29
Taking ln of both sides,
ln+%281%2F2%29+=+432k
k+=+%28ln+%281%2F2%29%29%2F432 = -0.00160...
Now, we substitute t = 343 years to our equation to obtain
A+=+45%2Ae%5E%28343%2A-.00160%29 = 25.95376 (grams)