0.022t The exponential model A = 752 e describes the population, A, of a country in millions, t.years after 2003. Use the model to determine when the population of the country will be 1362 million. The population of the country will be 1362 million in (Round to the nearest year as needed.) ...
0.022t The exponential model A = 752 e describes the population, A, of a country in millions, t.years after 2003. Use the model to determine when the population of the country will be 1362 million. The population of the country will be 1362 million in (Round to the nearest year as needed.) ...
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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![The exponential model \( A = 752e^{0.022t} \) describes the population, \( A \), of a country in millions, \( t \) years after 2003. Use the model to determine when the population of the country will be 1362 million.
---
The population of the country will be 1362 million in [ ].
(Round to the nearest year as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbac5cd56-9885-4a25-8e51-dfc1bb78a29e%2Fd1c9f413-5117-4495-b756-6599e3c95a76%2F3zrq8fb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The exponential model \( A = 752e^{0.022t} \) describes the population, \( A \), of a country in millions, \( t \) years after 2003. Use the model to determine when the population of the country will be 1362 million.
---
The population of the country will be 1362 million in [ ].
(Round to the nearest year as needed.)
![**Estimating the Age of Prehistoric Cave Paintings Using Carbon Dating**
Prehistoric cave paintings were discovered in a cave in France. The paint contained 21% 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.
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The paintings are approximately \([\text{Insert Calculation}]\) years old. (Round to the nearest integer.)
**Explanation:**
In this problem, we use the exponential decay formula, where:
- \( A \) is the remaining amount of carbon-14.
- \( A_0 \) is the initial amount of carbon-14.
- \( t \) is the time in years.
- The decay constant is \( -0.000121 \).
Given that the paint contains 21% of the original carbon-14, we have:
\[ A = 0.21 A_0 \]
By substituting into the exponential formula, we can solve for \( t \) to find the approximate age of the paintings.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbac5cd56-9885-4a25-8e51-dfc1bb78a29e%2Fd1c9f413-5117-4495-b756-6599e3c95a76%2Ffz47zf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Estimating the Age of Prehistoric Cave Paintings Using Carbon Dating**
Prehistoric cave paintings were discovered in a cave in France. The paint contained 21% 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 \([\text{Insert Calculation}]\) years old. (Round to the nearest integer.)
**Explanation:**
In this problem, we use the exponential decay formula, where:
- \( A \) is the remaining amount of carbon-14.
- \( A_0 \) is the initial amount of carbon-14.
- \( t \) is the time in years.
- The decay constant is \( -0.000121 \).
Given that the paint contains 21% of the original carbon-14, we have:
\[ A = 0.21 A_0 \]
By substituting into the exponential formula, we can solve for \( t \) to find the approximate age of the paintings.
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