The exponential function given by H(t) = 80,042.99(1.0484), where t is the number in 2040. The centenarian population in 2018 approximately. (Round to the nearest whole number.) The centenarian population in 2040 is approximately. (Round to the nearest whole number.) years after 2013, can be used to project the number of centenarians in a certain country. Use this function to project the centenarian population in this country in 2018 and
The exponential function given by H(t) = 80,042.99(1.0484), where t is the number in 2040. The centenarian population in 2018 approximately. (Round to the nearest whole number.) The centenarian population in 2040 is approximately. (Round to the nearest whole number.) years after 2013, can be used to project the number of centenarians in a certain country. Use this function to project the centenarian population in this country in 2018 and
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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![### Exponential Function for Projecting Centenarian Population
The exponential function given by:
\[ H(t) = 80,042.991(1.0484)^t \]
where \( t \) is the number of years after 2013, can be used to project the number of centenarians in a certain country. Use this function to project the centenarian population in this country in 2018 and in 2040.
1. **The centenarian population in 2018 is approximately:**
\[\text{(Round to the nearest whole number.)}\]
2. **The centenarian population in 2040 is approximately:**
\[\text{(Round to the nearest whole number.)}\]
**Instructions:**
1. To find the centenarian population in a given year, substitute the number of years after 2013 (i.e., \( t \)) into the exponential function.
2. For 2018, calculate \( t \) as \( 2018 - 2013 = 5 \) and substitute \( t = 5 \) into the function.
3. For 2040, calculate \( t \) as \( 2040 - 2013 = 27 \) and substitute \( t = 27 \) into the function.
**Example Calculation:**
To find the population in 2018:
\[ H(5) = 80,042.991 \times (1.0484)^5 \]
To find the population in 2040:
\[ H(27) = 80,042.991 \times (1.0484)^{27} \]
Make sure to round your final values to the nearest whole number.
After calculations, you can input your results in the respective fields and click the "Next" button to proceed.
**Graph Explanation:**
No graphs or diagrams are provided in this exercise. It consists solely of text instructions and mathematical formulas for calculation purposes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3230e3d-dd38-497e-8c1e-7c1c5570828c%2F2c0ca996-4230-4ab8-a07a-2f614c422fb3%2F6d5d2rf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Exponential Function for Projecting Centenarian Population
The exponential function given by:
\[ H(t) = 80,042.991(1.0484)^t \]
where \( t \) is the number of years after 2013, can be used to project the number of centenarians in a certain country. Use this function to project the centenarian population in this country in 2018 and in 2040.
1. **The centenarian population in 2018 is approximately:**
\[\text{(Round to the nearest whole number.)}\]
2. **The centenarian population in 2040 is approximately:**
\[\text{(Round to the nearest whole number.)}\]
**Instructions:**
1. To find the centenarian population in a given year, substitute the number of years after 2013 (i.e., \( t \)) into the exponential function.
2. For 2018, calculate \( t \) as \( 2018 - 2013 = 5 \) and substitute \( t = 5 \) into the function.
3. For 2040, calculate \( t \) as \( 2040 - 2013 = 27 \) and substitute \( t = 27 \) into the function.
**Example Calculation:**
To find the population in 2018:
\[ H(5) = 80,042.991 \times (1.0484)^5 \]
To find the population in 2040:
\[ H(27) = 80,042.991 \times (1.0484)^{27} \]
Make sure to round your final values to the nearest whole number.
After calculations, you can input your results in the respective fields and click the "Next" button to proceed.
**Graph Explanation:**
No graphs or diagrams are provided in this exercise. It consists solely of text instructions and mathematical formulas for calculation purposes.
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