Question
An artifact originally had 16 grams of carbon-14 present. The decay model Upper A equals 16 e Superscript negative 0.000121 t 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 5114 years.
Question content area bottom
Part 1
The amount of carbon-14 present in 5114 years will be approximately
enter your response here grams.
(Round to the nearest whole number.)
Question content area bottom
Part 1
The amount of carbon-14 present in 5114 years will be approximately
enter your response here grams.
(Round to the nearest whole number.)
Answers
GPT-4o mini
To find the amount of carbon-14 present after 5114 years using the decay model \( A = 16 e^{-0.000121t} \), we need to substitute \( t = 5114 \) into the formula.
Let's calculate it step-by-step:
1. Substitute \( t = 5114 \) into the equation:
\[
A = 16 e^{-0.000121 \cdot 5114}
\]
2. Calculate \( -0.000121 \cdot 5114 \):
\[
-0.000121 \cdot 5114 \approx -0.618034
\]
3. Now calculate \( e^{-0.618034} \):
\[
e^{-0.618034} \approx 0.538
\]
4. Finally, substitute this value back into the equation:
\[
A \approx 16 \cdot 0.538 \approx 8.608
\]
Rounding to the nearest whole number, the amount of carbon-14 present after 5114 years is approximately
\[
\boxed{9} \text{ grams}.
\]
Let's calculate it step-by-step:
1. Substitute \( t = 5114 \) into the equation:
\[
A = 16 e^{-0.000121 \cdot 5114}
\]
2. Calculate \( -0.000121 \cdot 5114 \):
\[
-0.000121 \cdot 5114 \approx -0.618034
\]
3. Now calculate \( e^{-0.618034} \):
\[
e^{-0.618034} \approx 0.538
\]
4. Finally, substitute this value back into the equation:
\[
A \approx 16 \cdot 0.538 \approx 8.608
\]
Rounding to the nearest whole number, the amount of carbon-14 present after 5114 years is approximately
\[
\boxed{9} \text{ grams}.
\]