Prehistoric cave paintings were discovered in a cave in France. The paint contained 34% of the original carbon-14. Use the exponential decay model for carbon-14, -0.000121t A = Ao e to estimate the age of the paintings. The paintings are approximately years old. (Round to the nearest integer.)

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Prehistoric cave paintings were discovered in a cave in France. The paint contained 34% of the original carbon-14. Use the exponential decay model for carbon-14, \( A = A_0 \, e^{-0.000121t} \), to estimate the age of the paintings.

The paintings are approximately \(\Box\) years old. (Round to the nearest integer.)

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**Explanation of Formula:**

- \( A \) represents the remaining amount of carbon-14.
- \( A_0 \) is the initial amount of carbon-14.
- \( e \) is the base of the natural logarithm.
- \( t \) denotes time, often measured in years.
- The decay constant \( 0.000121 \) is used to model the rate at which carbon-14 decays. 

In this problem, the exponential decay model helps determine how long it has been since the paintings were created based on the remaining carbon-14 content.
Transcribed Image Text:**Transcription for Educational Website:** --- Prehistoric cave paintings were discovered in a cave in France. The paint contained 34% of the original carbon-14. Use the exponential decay model for carbon-14, \( A = A_0 \, e^{-0.000121t} \), to estimate the age of the paintings. The paintings are approximately \(\Box\) years old. (Round to the nearest integer.) --- **Explanation of Formula:** - \( A \) represents the remaining amount of carbon-14. - \( A_0 \) is the initial amount of carbon-14. - \( e \) is the base of the natural logarithm. - \( t \) denotes time, often measured in years. - The decay constant \( 0.000121 \) is used to model the rate at which carbon-14 decays. In this problem, the exponential decay model helps determine how long it has been since the paintings were created based on the remaining carbon-14 content.
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