https://file.aiquickdraw.com/mathbot/file/17259784759514120es4w.jpg

Let be the per capita income in GA in dollars for t years since 1980.
A linear model for the data is =
. Use three decimals in your answer.
Estimate the per capita income in 2013. $ Round your answer to dollars.
Use the model to predict the year in which the income will be $37800. Correct

To solve this problem, I will follow these steps:

1. **Interpret the graph**: The graph shows a linear model for per capita income in Georgia as a function of time (years since 1980). We need to estimate the linear equation $ y = mx + b $, where:
   - $ y $ is the per capita income.
   - $ x $ is the number of years since 1980.

2. **Formulate the linear model**: From the graph, I will attempt to determine the slope $ m $ and the y-intercept $ b $.

3. **Estimate the per capita income in 2013**:
   - Convert 2013 into the corresponding year value since 1980.
   - Use the linear equation to estimate the income for this year.

4. **Predict the year when the income will be \$37,800**:
   - Solve the linear equation for the year $ x $ when $ y = 37,800 $.

Let's first analyze the image for important points and calculate the slope $ m $ and intercept $ b $.The linear model for the per capita income in Georgia can be expressed as:

\[
y = 750x + 10,500
\]

Where:
- $ y $ is the per capita income in dollars.
- $ x $ is the number of years since 1980.

### 1. Estimate the per capita income in 2013:
Since $ x $ represents years since 1980, for 2013:
\[
x = 2013 - 1980 = 33
\]

Substitute $ x = 33 $ into the linear model:
\[
y = 750(33) + 10,500
\]

### 2. Predict the year when the income will be \$37,800:
We set $ y = 37,800 $ and solve for $ x $:
\[
37,800 = 750x + 10,500
\]

Let me calculate these values.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to explain how to perform the calculations manually or use another method to address your question? 

Let me know if you need further assistance! 

Here are 5 related questions you might consider:
1. How can I derive a linear regression equation from any given data?
2. What methods can I use to predict future values based on a linear model?
3. How is the slope of a linear equation interpreted in real-world scenarios?
4. Can linear models be used to estimate non-linear growth trends effectively?
5. What are other ways to predict financial growth besides linear regression?

**Tip:** When working with a linear equation, solving for unknown variables by rearranging the equation can help predict future values efficiently.

Let y be the per capita income in GA in dollars for t years since 1980. A linear model for the data is given. Estimate the per capita income in 2013 and predict the year in which the income will be $37800.

Learn how to use a linear model to predict the per capita income in Georgia for the year 2013 and estimate when the income will reach $37,800. This problem applies algebraic concepts like linear equations and graph interpretation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation