SOLUTION: Plutonium-238 is used in bombs and power plants but is dangerously radioactive. It decays very slowly into nonradioactive materials. If you started with 300 grams today, a year fro

Question 1097074: Plutonium-238 is used in bombs and power plants but is dangerously radioactive. It decays very slowly into nonradioactive materials. If you started with 300 grams today, a year from now you would still have 297.6 grams.
a) Construct an exponential function to describe the decay of plutonium-238 over time, rounding to three decimal places if necessary: P(t)=?
b) How much of the original 300 grams of plutonium-238 would be left after 60 years? After 600 years?
Round the answers to one decimal place.
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
a)The formula for exponential decay is P(t)=P(0)*e^-kt, where P(t) is the amount after time t, P(0) is the original amount, and k is a constant. In this instance:
297.6=300*e^-k
.992=e^-k
ln 0.992=ln e^-k=-k ln e=-k
k=0.00803217169726425903864943221985
So P(t)=P(0)e^-0.008t
b) after 60 years:
P(60)=300*e^-0.008(60)=185.277 gms
P(600)=300*e^-0.008(600)=2.42172345 gms
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