The exponential function given by H(t)=80,040.23(1.0487), where t is the number of years after 2014, 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 2042. The centenarian population in 2018 is approximately (Round to the nearest whole number.) 11 The centenarian population in 2042 is approximately. (Round to the nearest whole number.)
The exponential function given by H(t)=80,040.23(1.0487), where t is the number of years after 2014, 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 2042. The centenarian population in 2018 is approximately (Round to the nearest whole number.) 11 The centenarian population in 2042 is approximately. (Round to the nearest whole number.)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:**Population Projection of Centenarians**
The exponential function given by \( H(t) = 80,040.23(1.0487)^t \), where \( t \) is the number of years after 2014, 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 2042.
1. The centenarian population in 2018 is approximately \(\_\_\_\).
(Round to the nearest whole number).
2. The centenarian population in 2042 is approximately \(\_\_\_\).
(Round to the nearest whole number).
**Educational Notes:**
- **Exponential Growth Function:** The given equation represents an exponential growth function, where:
- \( H(t) \) is the projected population of centenarians.
- \( 80,040.23 \) is the initial population size in the base year (2014).
- \( 1.0487 \) is the growth factor.
- \( t \) is the number of years after 2014.
- **Calculation:** To determine the population in a given year, substitute the year into the function and solve for \( H(t) \). For example:
- For 2018, \( t = 2018 - 2014 = 4 \).
- For 2042, \( t = 2042 - 2014 = 28 \).
- **Rounding:** Ensure to round the final answers to the nearest whole number for accuracy and practicality.
This information helps in understanding how populations change over time and can have various applications in fields such as demographics, public policy, and healthcare planning.
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