The decay of 192 mg of an isotope is given by A (t) = 192e-0.015t, where t is time in years. Find the amount left after 55 years. Round your answer to the nearest whole number.

Question

Sydney Baird

Mathematics

15 May, 16:37

The decay of 192 mg of an isotope is given by A (t) = 192e-0.015t, where t is time in years. Find the amount left after 55 years. Round your answer to the nearest whole number.

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Orlando Kaufman · Answer 1

This is a typical radioactive decay problem which uses the general form:

A = A0e^ (-kt)

So, in the given equation, A0 = 192 and k = 0.015. We are to find the amount of substance left after t = 55 years. That would be represented by A. The solution is as follows:

A = 192e^ (-0.015*55)

A = 84 mg