Question

an artifact originally had 16 grams of carbon - 14 present. the decay model a = 16e^(-0.000121t) describes the amount of carbon - 14 present after t years. use the model to determine how many grams of carbon - 14 will be present in 5932 years.
the amount of carbon - 14 present in 5932 years will be approximately grams.
(round to the nearest whole number.)

Explanation:

Step1: Substitute t value

Substitute $t = 5932$ into the formula $A = 16e^{-0.000121t}$. So we get $A=16e^{- 0.000121\times5932}$.

Step2: Calculate the exponent value

First, calculate $-0.000121\times5932=-0.717772$. Then we have $A = 16e^{-0.717772}$.

Step3: Calculate the exponential - function value

We know that $e^{-0.717772}\approx0.4877$. So $A = 16\times0.4877$.

Step4: Calculate the final value of A

$16\times0.4877 = 7.8032$. Rounding to the nearest whole number, we get $A\approx8$.

Answer:

8