SOLUTION: One of the main contaminants of a nuclear accident, such as that at Chernobyl, is strontium-90, which decays exponentially at an annual rate of approximately 2.8% per year. a. Wri

Question 1065660: One of the main contaminants of a nuclear accident, such as that at Chernobyl, is strontium-90, which decays exponentially at an annual rate of approximately 2.8% per year.
a. Write the percent of strontium-90 remaining, P, as a function of years, t, since the nuclear accident.
b.Estimate the half-life of strontium-90.
c.After the Chernobyl disaster, it was predicted that the region would not be safe for human habitation for 105 years. Estimate the percent of original strontium-90 remaining at this time.

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The general form of the exponential decay formula is
:
y = a(1-b)^x where y is final amount remaining after x time, a is the original amount and b is the rate of decay
:
for our problem we have
:
P = a * (1 - 0.028)^t / a
:
a) P = (1 - 0.028)^t
:
b) 0.50 = 0.972^t
:
use definition of logarithm
:
t = log(0.972) (0.50)
:
t = 24.401 approx 24.4 years
:
c) P = 0.972^105
:
P = 0.05069 approx 0.05 or 5%
:

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