SOLUTION: A 20-gram sample of uranium is decaying at a constant rate. After 5 days there are 19.6 grams of the uranium remaining. After 10 days there are 19.2 grams remaining. How much of

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A 20-gram sample of uranium is decaying at a constant rate. After 5 days there are 19.6 grams of the uranium remaining. After 10 days there are 19.2 grams remaining. How much of      Log On


   

Question 873540: A 20-gram sample of uranium is decaying at a constant rate. After 5 days there are 19.6 grams of the uranium remaining. After 10 days there are 19.2 grams remaining. How much of the sample remains after 30 days?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A 20-gram sample of uranium is decaying at a constant rate.
After 5 days there are 19.6 grams of the uranium remaining.
:
We can find the half-life of the substance with this information using the formula
Ao*2^(-t/h) = A, where:
Ao = initial amt
t = time
h = half-life of substance
A = resulting amt after t time
:
20*2(-5/h) = 19.6
2^(-5/h) = 19.6%2F20
2^(-5/h) = .98
-5%2Fh = ln%28.98%29%2Fln%282%29
-5%2Fh = -.029146
h = %28-5%29%2F%28-.029146%29
h = 171.55 days is the half life of the substance
:
After 10 days there are 19.2 grams remaining.
How much of the sample remains after 30 days?
t = 30
A = 20*2(-30/171.55)
A = 17.7 grams remain after 30 days