
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
![### 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.](https://content.bartleby.com/qna-images/question/8ad87420-52d2-4e34-815e-eb9bcb5c95c0/446b3765-f78e-4d02-9998-bfb411ca2c6a/yghpc2d_thumbnail.png)
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.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 4 steps

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- How long will it take 72 grams of magnesium-28 to decay into the following amounts? (a) 36 grams(b) 18 grams(c) 9 gramsarrow_forwardSuppose a radioactive substance decays at a continuous rate of 6% per year. How long will it be until only 30% of the original amount remains? Round your answer in years to the nearest hundredth (i.e., two decimal places). Enter number only, e.g. if your answer is 25.69 years, enter 25.69.arrow_forwardAn unknown radioactive element decays into non-radioactive substances. In 580 days the radioactivity of a sample decreases by 62 percent. (a) Find the decay constant k. (Round your answer to 5 decimal places.) (b) What is the half-life of the element? (Round your answer to two decimal places) half-life: (days) (c) How long will it take for a sample of 100 mg to decay to 83 mg? (Round your answer to two decimal places) time needed: (days)arrow_forward
Recommended textbooks for you
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning

Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning

Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON

Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON

Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman


Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning