A city has a population of 210,000 people. Suppose that each year the population grows by 6.5%. What will the population be after 13 years? Use the calculator provided and round your answer to the nearest whole number. people X
A city has a population of 210,000 people. Suppose that each year the population grows by 6.5%. What will the population be after 13 years? Use the calculator provided and round your answer to the nearest whole number. people X
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Population Growth Question
**Problem Statement:**
A city has a population of 210,000 people. Suppose that each year the population grows by 6.5%. What will the population be after 13 years?
Use the calculator provided and round your answer to the nearest whole number.
**Calculation Instructions:**
Below the problem statement, there is an input box labeled "people" where you can enter your calculations. Next to this input box, there are two buttons:
- A button marked with an "X" icon, likely for clearing the input.
- A button marked with a refresh icon, possibly for recalculating or resetting the function.
**Solution Approach:**
To find the population after 13 years given an annual growth rate of 6.5%, use the formula for compound growth:
\[ P(t) = P_0 (1 + r)^t \]
Where:
- \( P(t) \) is the population after time \( t \).
- \( P_0 \) is the initial population (210,000 people).
- \( r \) is the growth rate (6.5% or 0.065).
- \( t \) is the number of years (13 years).
Plugging in the values, the equation becomes:
\[ P(13) = 210,000 (1 + 0.065)^{13} \]
Perform this calculation to get the final population figure, and then round it to the nearest whole number.
### Graphs and Diagrams
There are no graphs or diagrams provided in the problem statement. The focus is on using the calculator to determine the population after the specified period.
**Note:** Make sure to use the appropriate tools to calculate the compounded population growth accurately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec8216c7-9603-414d-880e-1b2c9e8c3a03%2F6a93689a-55e7-409b-b8e1-b84ddbfef6ae%2F7zyrw0a_processed.png&w=3840&q=75)
Transcribed Image Text:### Population Growth Question
**Problem Statement:**
A city has a population of 210,000 people. Suppose that each year the population grows by 6.5%. What will the population be after 13 years?
Use the calculator provided and round your answer to the nearest whole number.
**Calculation Instructions:**
Below the problem statement, there is an input box labeled "people" where you can enter your calculations. Next to this input box, there are two buttons:
- A button marked with an "X" icon, likely for clearing the input.
- A button marked with a refresh icon, possibly for recalculating or resetting the function.
**Solution Approach:**
To find the population after 13 years given an annual growth rate of 6.5%, use the formula for compound growth:
\[ P(t) = P_0 (1 + r)^t \]
Where:
- \( P(t) \) is the population after time \( t \).
- \( P_0 \) is the initial population (210,000 people).
- \( r \) is the growth rate (6.5% or 0.065).
- \( t \) is the number of years (13 years).
Plugging in the values, the equation becomes:
\[ P(13) = 210,000 (1 + 0.065)^{13} \]
Perform this calculation to get the final population figure, and then round it to the nearest whole number.
### Graphs and Diagrams
There are no graphs or diagrams provided in the problem statement. The focus is on using the calculator to determine the population after the specified period.
**Note:** Make sure to use the appropriate tools to calculate the compounded population growth accurately.
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