Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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### Carbon-14 Decay Model

The rate at which a sample of \( ^{14}\text{C} \) (Carbon-14) decays can be modeled using the following function:

\[ 
r(t) = -0.027205(0.998188^t) \text{ grams per year}
\]

where \( t \) is the number of years since the sample began decaying.

#### Exercises

(a) **Decay in the First 1000 Years:**
- Calculate how much of the \( ^{14}\text{C} \) will decay during the first 1000 years.
- Round your answer to three decimal places.
- Answer: ______ g

(b) **Decay in the Fourth 1000-Year Period:**
- Determine how much of the \( ^{14}\text{C} \) will decay during the fourth 1000 years.
- Round your answer to four decimal places.
- Answer: ______ g

(c) **Total Decay:**
- Compute how much of the \( ^{14}\text{C} \) will eventually decay.
- Round your answer to three decimal places.
- Answer: ______ g

This exercise helps in understanding exponential decay and its application in radiocarbon dating.
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Transcribed Image Text:### Carbon-14 Decay Model The rate at which a sample of \( ^{14}\text{C} \) (Carbon-14) decays can be modeled using the following function: \[ r(t) = -0.027205(0.998188^t) \text{ grams per year} \] where \( t \) is the number of years since the sample began decaying. #### Exercises (a) **Decay in the First 1000 Years:** - Calculate how much of the \( ^{14}\text{C} \) will decay during the first 1000 years. - Round your answer to three decimal places. - Answer: ______ g (b) **Decay in the Fourth 1000-Year Period:** - Determine how much of the \( ^{14}\text{C} \) will decay during the fourth 1000 years. - Round your answer to four decimal places. - Answer: ______ g (c) **Total Decay:** - Compute how much of the \( ^{14}\text{C} \) will eventually decay. - Round your answer to three decimal places. - Answer: ______ g This exercise helps in understanding exponential decay and its application in radiocarbon dating.
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