Math problem about strontium-90?

Question

One of the main contaminants of a nuclear accident, such as that at Chernobyl, is strontium-90, which decays exponentially at a rate of approximately 2.5% 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 strontium-90

c) After the Chernobyl disaster, it wa spredicted that the region would not be safe for human habitation for 100 years. Estimate the percent of original strontium-90 remaining at this time.

Answer 1

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After one year, fraction remaining = (1 - 0.025) = 0.975

After two years, fraction remaining = 0.975 x 0.975

After three years, fraction remaining = 0.975 x 0.975 x 0.975

and so on.

So after t years, fraction remaining = 0.975^t

or, as a percentage, = 0.975^t x 100

Half life is the time for the remainder to drop to 0.5

So

0.975^t = 0.5

t log 0.975 = log 0.5

t = log 0.5 / log 0.975 = 27.378 years

At t = 100 years

P = 0.975^100 = 0.0795