Suppose a fish population is currently 7000 and 5 years later the population is 11000. Use the explicit exponential model to find the rate of growth. Express the rate of growth as a percentage. Round to the nearest tenth. T= % Calculator
Suppose a fish population is currently 7000 and 5 years later the population is 11000. Use the explicit exponential model to find the rate of growth. Express the rate of growth as a percentage. Round to the nearest tenth. T= % Calculator
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![### Finding the Rate of Growth Using an Exponential Model
#### Problem Statement:
Suppose a fish population is currently 7000 and 5 years later the population is 11000. Use the explicit exponential model to find the rate of growth.
#### Instructions:
- Express the rate of growth as a percentage.
- Round to the nearest tenth.
#### Formula:
To find the rate of growth, we use the exponential growth formula:
\[ P(t) = P_0 \times e^{rt} \]
Where:
- \( P(t) \) is the population at time \( t \).
- \( P_0 \) is the initial population.
- \( r \) is the rate of growth.
- \( t \) is the time in years.
#### Given:
- Initial Population, \( P_0 = 7000 \)
- Population after 5 years, \( P(5) = 11000 \)
- Time, \( t = 5 \) years
#### Steps to Calculate:
1. Substitute the values into the growth formula:
\[ 11000 = 7000 \times e^{5r} \]
2. Rearrange to solve for \( r \):
\[ \frac{11000}{7000} = e^{5r} \]
\[ \ln\left(\frac{11000}{7000}\right) = 5r \]
\[ r = \frac{1}{5} \ln\left(\frac{11000}{7000}\right) \]
3. Use a calculator to find the value of \( r \).
#### Answer Input Box:
- Enter the calculated rate of growth \( r \) as a percentage.
- Round to the nearest tenth.
\[ r = \]
\[ \text{Percentage } (\%) \]
#### Submit Your Answer:
- Once you have calculated the value, enter it into the box and click on the "Submit Question" button.
#### Additional Tools:
- A calculator button is provided for your convenience to help with the calculations.
#### Example Calculation:
\[ e^{-2} = \frac{1}{e^2} \]
Click on the “Submit Question” button after entering your answer.
---
This format ensures the information is clear and accessible for students learning about exponential growth models.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd5f5ee9-7826-4954-8faf-403f1f0e24a3%2F2fe135cf-4baa-470d-a28b-6687347ec491%2F6488m4v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Rate of Growth Using an Exponential Model
#### Problem Statement:
Suppose a fish population is currently 7000 and 5 years later the population is 11000. Use the explicit exponential model to find the rate of growth.
#### Instructions:
- Express the rate of growth as a percentage.
- Round to the nearest tenth.
#### Formula:
To find the rate of growth, we use the exponential growth formula:
\[ P(t) = P_0 \times e^{rt} \]
Where:
- \( P(t) \) is the population at time \( t \).
- \( P_0 \) is the initial population.
- \( r \) is the rate of growth.
- \( t \) is the time in years.
#### Given:
- Initial Population, \( P_0 = 7000 \)
- Population after 5 years, \( P(5) = 11000 \)
- Time, \( t = 5 \) years
#### Steps to Calculate:
1. Substitute the values into the growth formula:
\[ 11000 = 7000 \times e^{5r} \]
2. Rearrange to solve for \( r \):
\[ \frac{11000}{7000} = e^{5r} \]
\[ \ln\left(\frac{11000}{7000}\right) = 5r \]
\[ r = \frac{1}{5} \ln\left(\frac{11000}{7000}\right) \]
3. Use a calculator to find the value of \( r \).
#### Answer Input Box:
- Enter the calculated rate of growth \( r \) as a percentage.
- Round to the nearest tenth.
\[ r = \]
\[ \text{Percentage } (\%) \]
#### Submit Your Answer:
- Once you have calculated the value, enter it into the box and click on the "Submit Question" button.
#### Additional Tools:
- A calculator button is provided for your convenience to help with the calculations.
#### Example Calculation:
\[ e^{-2} = \frac{1}{e^2} \]
Click on the “Submit Question” button after entering your answer.
---
This format ensures the information is clear and accessible for students learning about exponential growth models.
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