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# Applications of Exponents 11

ALGEBR-4GGCC4

Archaeologists and anthropologists are using radioactive decay to predict how long ago an organism died. This method is called radiocarbon dating. The radioactive decay is usually modeled by an exponential function, as carbon dating is based upon the decay of $^{14}C$.

The equation for carbon dating is $N(t) = N_0e^{- 0.0001216 t}$, while $N_0$ is the initial amount of $^{14}C$ when $t = 0$ and $t$ is measured in years.

If there are 7.8 g remaining after 18000 years, approximately how many grams of $^{14}C$ did the organism initially possess?

A

10.78

B

12.66

C

14.73

D

16.54