The rate at which a sample of 14C is decaying can be modeled as r(t) = -0.027205(0.998188*) grams per year where t is the number of years since the sample began decaying. (a) How much of the 14C will decay during the first 1000 years? (Round your answer to three decimal places.) How much of the 14C will decay during the fourth 1000 years? (Round your answer to four decimal places.) (b) How much of the 14c will eventually decay? (Round your answer to three decimal places.)
The rate at which a sample of 14C is decaying can be modeled as r(t) = -0.027205(0.998188*) grams per year where t is the number of years since the sample began decaying. (a) How much of the 14C will decay during the first 1000 years? (Round your answer to three decimal places.) How much of the 14C will decay during the fourth 1000 years? (Round your answer to four decimal places.) (b) How much of the 14c will eventually decay? (Round your answer to three decimal places.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
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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![### 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ad87420-52d2-4e34-815e-eb9bcb5c95c0%2F446b3765-f78e-4d02-9998-bfb411ca2c6a%2Fyghpc2d_processed.png&w=3840&q=75)
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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