The fox population in a certain region has an annual growth rate of 8 percent per year. It is estimated that the population in the year 2000 was 22300. (a) Find a function that models the population t years after 2000 (t = 0 for 2000). Your answer is P(t) = %3D (b) Use the function from part (a) to estimate the fox population.in the year 2008. Your answer is (the answer should be an integer) Question Help: DVideo
The fox population in a certain region has an annual growth rate of 8 percent per year. It is estimated that the population in the year 2000 was 22300. (a) Find a function that models the population t years after 2000 (t = 0 for 2000). Your answer is P(t) = %3D (b) Use the function from part (a) to estimate the fox population.in the year 2008. Your answer is (the answer should be an integer) Question Help: DVideo
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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![**Problem Statement: Fox Population Growth Model**
The fox population in a certain region has an annual growth rate of 8 percent per year. It is estimated that the population in the year 2000 was 22,300.
**Tasks:**
(a) **Find a Function:**
- Develop a function that models the population \( t \) years after 2000 (\( t = 0 \) for the year 2000).
- Function required: \( P(t) = \_\_\_\_ \)
(b) **Estimate Future Population:**
- Use the function from part (a) to estimate the fox population in the year 2008.
- The answer should be an integer.
**Solution Process:**
1. The growth of the fox population can be modeled using an exponential function:
\[
P(t) = P_0 (1 + r)^t
\]
Where:
- \( P_0 \) is the initial population (22,300 in the year 2000).
- \( r \) is the growth rate (8% or 0.08).
- \( t \) is the number of years since the year 2000.
2. Substitute the given values to model the function for part (a).
3. To solve part (b), substitute \( t = 8 \) (for the year 2008) into the function to estimate the population, and round the result to the nearest integer.
**Note:**
- Ensure calculations are precise and verify accuracy using appropriate computational tools.
- Additional resources such as video tutorials can be accessed for further understanding.
**Utility Options:**
- For any assisting queries, select "Question Help" and choose the video option.
- Ensure to click "Submit Question" once the answer is finalized.
This exercise enhances understanding of exponential growth models and their application in real-world scenarios, valuable for mathematical and statistical studies.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2eab21cb-1cbc-4339-9c62-335ff85c7618%2F56154f41-497a-4194-9507-3d8ab640e8c5%2Fyloecj8.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement: Fox Population Growth Model**
The fox population in a certain region has an annual growth rate of 8 percent per year. It is estimated that the population in the year 2000 was 22,300.
**Tasks:**
(a) **Find a Function:**
- Develop a function that models the population \( t \) years after 2000 (\( t = 0 \) for the year 2000).
- Function required: \( P(t) = \_\_\_\_ \)
(b) **Estimate Future Population:**
- Use the function from part (a) to estimate the fox population in the year 2008.
- The answer should be an integer.
**Solution Process:**
1. The growth of the fox population can be modeled using an exponential function:
\[
P(t) = P_0 (1 + r)^t
\]
Where:
- \( P_0 \) is the initial population (22,300 in the year 2000).
- \( r \) is the growth rate (8% or 0.08).
- \( t \) is the number of years since the year 2000.
2. Substitute the given values to model the function for part (a).
3. To solve part (b), substitute \( t = 8 \) (for the year 2008) into the function to estimate the population, and round the result to the nearest integer.
**Note:**
- Ensure calculations are precise and verify accuracy using appropriate computational tools.
- Additional resources such as video tutorials can be accessed for further understanding.
**Utility Options:**
- For any assisting queries, select "Question Help" and choose the video option.
- Ensure to click "Submit Question" once the answer is finalized.
This exercise enhances understanding of exponential growth models and their application in real-world scenarios, valuable for mathematical and statistical studies.
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