SOLUTION: help me please The half-life of a certain radioactive material is 66 days. An initial amount of the material has a mass of 474 kg. Write an exponential function that models the

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: help me please The half-life of a certain radioactive material is 66 days. An initial amount of the material has a mass of 474 kg. Write an exponential function that models the      Log On


   

Question 469358: help me please
The half-life of a certain radioactive material is 66 days. An initial amount of the material has a mass of 474 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 9 days. Round your answer to the nearest thousandth.
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
General exponential function:
P%28t%29+=+P%2Ae%5Ekt
where P is initial value, t is time, k is constant
For this problem we know P and t
P = 474
t = 9
However, k is unknown, but they tell us that when t=66, P(t) = P/2
Half-life just means you have half what you started with
Using this we can solve for k:
474%2F2+=+474%2Ae%5E%2866k%29
Divide by 474 on both sides
1%2F2+=+e%5E%2866k%29
Take natural log of both sides: ln(e^a) = a
ln%281%2F2%29+=+66k
Divide by 66 on both sides
%28ln%281%2F2%29%29%2F66+=+k
Use scientific calculator to approximate
k+=+-.0105
Now substitute this in for k in general equation to solve for P(9)
P%289%29+=+474%2Ae%5E%28-.0105%2A9%29
P%289%29+=+431.25