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Algebra

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Applications of Exponents 2

ALGEBR-KCGGCK

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

Carbon dating is based upon the decay of the Carbon-14 isotope $^{14}C$. 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.

Suppose an organism has $20\ grams$ of $^{14}C$ at its time of death.

Approximately how many grams of $^{14}C$ will remain after $10320\ years$?​

A

$5.7$

B

$0.3$

C

$0.002$

D

$17.6$