23 a. Use the data points (7, 15400) and (13, 22600) to write a linear model of the form: f(t)=mt + b where t is the number of years after 2000 and b is the population in 2000. 15400= m 7+16 7200=6m 22600=m. 13+b m=100 15400 = 1200.7+b f()=1200+ b =15400-8400=7000 b. Use the model from (a) to approximate the population in 2020
23 a. Use the data points (7, 15400) and (13, 22600) to write a linear model of the form: f(t)=mt + b where t is the number of years after 2000 and b is the population in 2000. 15400= m 7+16 7200=6m 22600=m. 13+b m=100 15400 = 1200.7+b f()=1200+ b =15400-8400=7000 b. Use the model from (a) to approximate the population in 2020
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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Question
Please solve part B, if part A is incorrect solve both.
![**Transcription and Explanation**
**Title: Creating a Linear Model for Population Growth**
**Objective:**
- Use given data points to write a linear model to predict population growth.
- Approximate future population using the model.
**Instructions:**
**a. Use the data points (7, 15400) and (13, 22600) to write a linear model of the form:**
\[ f(t) = mt + b \]
where \( t \) is the number of years after 2000, and \( b \) is the population in 2000.
**Solution:**
- Set up the equations using the given points:
1. \( 15400 = m \cdot 7 + b \)
2. \( 22600 = m \cdot 13 + b \)
- Solve the equations to find \( m \) and \( b \):
- Subtract the first equation from the second:
\[
22600 - 15400 = m \cdot (13 - 7)
\]
\[
7200 = 6m
\]
\[
m = 1200
\]
- Substitute \( m = 1200 \) back into the first equation:
\[
15400 = 1200 \cdot 7 + b
\]
\[
15400 = 8400 + b
\]
\[
b = 7000
\]
- The linear model is:
\[
f(t) = 1200t + 7000
\]
**Graphical Representation:**
- The linear equation represents a graph where the y-axis is the population, and the x-axis is the number of years after 2000.
**b. Use the model from (a) to approximate the population in 2020:**
- Calculate for \( t = 20 \) (since 2020 is 20 years after 2000):
\[
f(20) = 1200 \cdot 20 + 7000
\]
\[
f(20) = 24000 + 7000
\]
\[
f(20) = 31000
\]
**Conclusion:**
The approximate population in 2020, using the linear](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16698408-ee4b-436e-ae87-879a478aa341%2F381bf0b5-fd16-4536-bf39-8f5a83712aeb%2Fg9j4aqq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription and Explanation**
**Title: Creating a Linear Model for Population Growth**
**Objective:**
- Use given data points to write a linear model to predict population growth.
- Approximate future population using the model.
**Instructions:**
**a. Use the data points (7, 15400) and (13, 22600) to write a linear model of the form:**
\[ f(t) = mt + b \]
where \( t \) is the number of years after 2000, and \( b \) is the population in 2000.
**Solution:**
- Set up the equations using the given points:
1. \( 15400 = m \cdot 7 + b \)
2. \( 22600 = m \cdot 13 + b \)
- Solve the equations to find \( m \) and \( b \):
- Subtract the first equation from the second:
\[
22600 - 15400 = m \cdot (13 - 7)
\]
\[
7200 = 6m
\]
\[
m = 1200
\]
- Substitute \( m = 1200 \) back into the first equation:
\[
15400 = 1200 \cdot 7 + b
\]
\[
15400 = 8400 + b
\]
\[
b = 7000
\]
- The linear model is:
\[
f(t) = 1200t + 7000
\]
**Graphical Representation:**
- The linear equation represents a graph where the y-axis is the population, and the x-axis is the number of years after 2000.
**b. Use the model from (a) to approximate the population in 2020:**
- Calculate for \( t = 20 \) (since 2020 is 20 years after 2000):
\[
f(20) = 1200 \cdot 20 + 7000
\]
\[
f(20) = 24000 + 7000
\]
\[
f(20) = 31000
\]
**Conclusion:**
The approximate population in 2020, using the linear
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