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 9825 years.
the amount of carbon - 14 present in 9825 years will be approximately (square) grams.
(round to the nearest whole number.)

Explanation:

Step1: Substitute \( t = 9825 \) into the formula

Given the formula \( A=16e^{- 0.000121t} \), when \( t = 9825 \), we have \( A = 16e^{-0.000121\times9825} \).
First, calculate the exponent: \( -0.000121\times9825=-1.188825 \).
So, \( A = 16e^{-1.188825} \).

Step2: Calculate the value of \( e^{-1.188825} \)

We know that \( e^{-x}=\frac{1}{e^{x}} \). Using a calculator, \( e^{-1.188825}\approx0.304 \).

Step3: Calculate the value of \( A \)

Then \( A = 16\times0.304 = 4.864\).

Answer:

\( 5 \)