SOLUTION: Hey guys, I was wondering if you guys could help me or guide me thru these questions, thanks for your time. The half-life of radioactive plutonium-238 is 87.7 years. If ten gra

Algebra ->  Finance -> SOLUTION: Hey guys, I was wondering if you guys could help me or guide me thru these questions, thanks for your time. The half-life of radioactive plutonium-238 is 87.7 years. If ten gra      Log On


   

Question 928040: Hey guys, I was wondering if you guys could help me or guide me thru these questions, thanks for your time.
The half-life of radioactive plutonium-238 is 87.7 years. If ten grams are present now:
a) Build an exponential function that models the amount of plutonium-238 after t years.
b) Use your function to determine the amount of plutonium-238 remaining after 200 years. Solve this algebraically.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
the half-life of radioactive plutonium-238 is 87.7 years
and starting amount 10gr

a) Build an exponential function that models the amount of plutonium-238 after t years.

A=A%5Bo%5D%280.5%29%5E%28t%2F87.7+%29 ...where A - amount after t years , A%5Bo%5D -amount started with

b) Use your function to determine the amount of plutonium-238 remaining after 200 years. Solve this algebraically.

A%5Bo%5D=10gr
t=200 years
A=10%280.5%29%5E%28%28200cross%28years%29%29%2F%2887.7cross%28years%29%29+%29...since exponent is not visible here, it is %28200cross%28years%29%29%2F%2887.7cross%28years%29%29=2.280501710376283+

A=10gr%280.5%29%5E%282.280501710376283+%29+
A=10gr%280.205826%29
A=2.05826gr