D. 15,000 years
You want to find t such that ...
... 0.155 = e^(-0.000124t)
Take the natural logarithm of both sides and divide by the coefficient of t.
... ln(0.155) = -0.000124t
... -1.86433/-0.000124 = t ≈ 15,034.9
Rounded to 3 significant figures, the age is 15,000 years.
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Comment on aswer precision
Each of the supplied numbers (15.5% and -0.000124) have 3 significant digits. Their accuracy results in a possible age range from 14,949 years to 15,122 years. Certainly, the answer 15,035 years is not supported by this level of precision in the numbers. The answer is best rounded to 3 significant digits: 1.50×10^4 years, or 15,000 years.
