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Algebra

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Applications of Logarithms - Radioactive Decay

ALGEBR-FXJ9EC

Archaeologists and anthropologists use radioactive decay to calculate how long ago an organism died. This method is called radiocarbon dating. Radioactive decay is usually modeled by exponential functions.

Carbon dating is based upon the decay of $^{14}C$; the equation for carbon dating is:​

$$N(t) = N_0e^{- 0.0001216 t}$$

where $N_0$ is the initial amount of $^{14}C$ when $t = 0$ and $t$ is measured in years.

Approximately how old (in years) is a fossil with 12 g of $^{14}C$, if it initially possessed 32 g of $^{14}C$ ?

A

5,600

B

6,780

C

7,500

D

8,066