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 7386 years.
the amount of carbon-14 present in 7386 years will be approximately \boxed{} grams.
(round to the nearest whole number.)

Explanation:

Step1: Identify the formula and values

The decay model is \( A = 16e^{-0.000121t} \), where \( t = 7386 \) years.

Step2: Substitute \( t \) into the formula

Calculate the exponent first: \( -0.000121 \times 7386 \approx -0.8937 \)
Then, find \( e^{-0.8937} \approx 0.409 \) (using a calculator for the exponential function)

Step3: Calculate \( A \)

Multiply by the initial amount: \( A = 16 \times 0.409 \approx 6.544 \)

Step4: Round to the nearest whole number

\( 6.544 \) rounded to the nearest whole number is 7.

Answer:

7