Thank you for visiting The table below shows the United States federal education spending in billions of dollars for selected years tex begin tabular l l hline 2012 109. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To solve this problem, we need to find a linear function [tex]\( S(t) \)[/tex] that models the given spending data over the years, where [tex]\( t \)[/tex] is the number of years since 2011. The data provided includes the amounts of federal education spending in billions of dollars from 2012 to 2017.
Here's how you can determine the function [tex]\( S(t) \)[/tex]:
1. Assign Values to [tex]\( t \)[/tex]:
- Since [tex]\( t = 1 \)[/tex] corresponds to 2011, [tex]\( t = 2 \)[/tex] corresponds to 2012, and so on. Therefore:
- 2012 is [tex]\( t = 2 \)[/tex]
- 2013 is [tex]\( t = 3 \)[/tex]
- 2014 is [tex]\( t = 4 \)[/tex]
- 2015 is [tex]\( t = 5 \)[/tex]
- 2016 is [tex]\( t = 6 \)[/tex]
- 2017 is [tex]\( t = 7 \)[/tex]
2. Create Data Points:
- Pair the values of [tex]\( t \)[/tex] with the corresponding spending amounts:
- [tex]\( (2, 109.3) \)[/tex]
- [tex]\( (3, 105.1) \)[/tex]
- [tex]\( (4, 104.5) \)[/tex]
- [tex]\( (5, 99.0) \)[/tex]
- [tex]\( (6, 99.3) \)[/tex]
- [tex]\( (7, 97.7) \)[/tex]
3. Perform Linear Regression:
- A linear regression will provide us with a line of best fit through these points. The equation of a line is typically given by:
[tex]\[ S(t) = mt + b \][/tex]
- Here, [tex]\( m \)[/tex] is the slope of the line, and [tex]\( b \)[/tex] is the y-intercept.
4. Results from Linear Regression:
- The calculations give us the slope [tex]\( m \)[/tex] and the y-intercept [tex]\( b \)[/tex] as follows:
- Slope [tex]\( m = -2.31 \)[/tex]
- Y-intercept [tex]\( b = 112.88 \)[/tex]
5. Write the Function:
- Now, substitute [tex]\( m \)[/tex] and [tex]\( b \)[/tex] into the linear equation:
[tex]\[ S(t) = -2.31t + 112.88 \][/tex]
This equation [tex]\( S(t) = -2.31t + 112.88 \)[/tex] represents the model for the federal education spending, in billions of dollars, where [tex]\( t \)[/tex] is the number of years since 2011.
Here's how you can determine the function [tex]\( S(t) \)[/tex]:
1. Assign Values to [tex]\( t \)[/tex]:
- Since [tex]\( t = 1 \)[/tex] corresponds to 2011, [tex]\( t = 2 \)[/tex] corresponds to 2012, and so on. Therefore:
- 2012 is [tex]\( t = 2 \)[/tex]
- 2013 is [tex]\( t = 3 \)[/tex]
- 2014 is [tex]\( t = 4 \)[/tex]
- 2015 is [tex]\( t = 5 \)[/tex]
- 2016 is [tex]\( t = 6 \)[/tex]
- 2017 is [tex]\( t = 7 \)[/tex]
2. Create Data Points:
- Pair the values of [tex]\( t \)[/tex] with the corresponding spending amounts:
- [tex]\( (2, 109.3) \)[/tex]
- [tex]\( (3, 105.1) \)[/tex]
- [tex]\( (4, 104.5) \)[/tex]
- [tex]\( (5, 99.0) \)[/tex]
- [tex]\( (6, 99.3) \)[/tex]
- [tex]\( (7, 97.7) \)[/tex]
3. Perform Linear Regression:
- A linear regression will provide us with a line of best fit through these points. The equation of a line is typically given by:
[tex]\[ S(t) = mt + b \][/tex]
- Here, [tex]\( m \)[/tex] is the slope of the line, and [tex]\( b \)[/tex] is the y-intercept.
4. Results from Linear Regression:
- The calculations give us the slope [tex]\( m \)[/tex] and the y-intercept [tex]\( b \)[/tex] as follows:
- Slope [tex]\( m = -2.31 \)[/tex]
- Y-intercept [tex]\( b = 112.88 \)[/tex]
5. Write the Function:
- Now, substitute [tex]\( m \)[/tex] and [tex]\( b \)[/tex] into the linear equation:
[tex]\[ S(t) = -2.31t + 112.88 \][/tex]
This equation [tex]\( S(t) = -2.31t + 112.88 \)[/tex] represents the model for the federal education spending, in billions of dollars, where [tex]\( t \)[/tex] is the number of years since 2011.
Thank you for reading the article The table below shows the United States federal education spending in billions of dollars for selected years tex begin tabular l l hline 2012 109. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
