SOLUTION: I need on how to solve this. Please show work. Thanks! The Radioactive element americium-241 has a half-life of 432 years. Suppose we start with a 45-g mass of americim-241. How

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: I need on how to solve this. Please show work. Thanks! The Radioactive element americium-241 has a half-life of 432 years. Suppose we start with a 45-g mass of americim-241. How      Log On


   

Question 328263: I need on how to solve this. Please show work. Thanks!
The Radioactive element americium-241 has a half-life of 432 years. Suppose we start with a 45-g mass of americim-241. How much will be left after 329 years? compute the answer to three significant digits.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Radioactive decay problems are modeled using an exponential function,
N%28t%29=N0%2Ae%5E%28kt%29
where N0 is the initial amount of material, k is a constant for each material.
Half life means that 1/2 of the initial amount remains.
We use this to calculate k.
%281%2F2%29N0=N0%2Ae%5E%28k%28432%29%29
e%5E%28432k%29=%281%2F2%29
432k=ln%281%2F2%29
k=ln%281%2F2%29%2F432=-1.605x10%5E%28-3%29
.
.
.
So now find N(329).
kt=%28329%29%28-1.605x10%5E%28-3%29%29=-0.527883
N%28329%29=45%2Ae%5E%28-0.527883%29
N%28329%29=45%2A%280.58985%29
N%28329%29=26.543grams