Using an Exponential Decay Formula

Carbon dating is used by scientists to find the age of fossils, bones, and other items. The formula used in carbon dating is

P(t) = $P_02^{-t/5600}$

where $P_0$ represents the original amount of carbon-14 ( $C_{14}$ ) present and P(t) represents the amount of $C_{14}$ present after t years. If 10 mg of $C_{14}$ is present in an animal bone recently excavated, how many milligrams will be present in 3000 years?

Question

Using an Exponential Decay Formula

Carbon dating is used by scientists to find the age of fossils, bones, and other items. The formula used in carbon dating is

P(t) = [latex]P_02^{-t/5600}[/latex]

where [latex]P_0[/latex] represents the original amount of carbon-14 ([latex]C_{14}[/latex]) present and P(t) represents the amount of [latex]C_{14}[/latex] present after t years. If 10 mg of [latex]C_{14}[/latex] is present in an animal bone recently excavated, how many milligrams will be present in 3000 years?

Accepted Answer

Substituting the values in the formula gives

P(t) = [latex]P_02^{-t/5600}[/latex]

P(3000) = [latex]10(2)^{-3000/5600}[/latex]

≈ [latex]10(2)^{-0.54}[/latex] (Recall that ≈ means “is approximately equal to.”)

≈ 10(0.69)

≈ 6.9 mg

Thus, in 3000 years, approximately 6.9 mg of the original 10 mg of [latex]C_{14}[/latex] will remain.

Question 6.10.8: Using an Exponential Decay Formula Carbon dating is used by ......

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