The amount of carbon-14 present in animal bones after $t$ years is given by $A(t)=A_{0} e^{-0.00012 t}$. A sample of fossil had $12 \%$ of the carbon 14 of a contemporary living sample. Estimate the age of the sample.

The age of the sample is $\square$ years.
(Round to the nearest year as needed.)

Answer

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Answer

Round to the nearest year: $\boxed{18408}$

Steps

Step 1 ：$0.12 = e^{-0.00012t}$

Step 2 ：Take the natural logarithm of both sides: $\ln(0.12) = -0.00012t$

Step 3 ：Divide both sides by -0.00012 to isolate t: $t = \frac{\ln(0.12)}{-0.00012}$

Step 4 ：Calculate t: $t \approx 18407.5$

Step 5 ：Round to the nearest year: $\boxed{18408}$