The following table gives the millions of metric tons of carbon dioxide emissions in a certain country for selected years from 2010 and projected to 2032.
Year	2010	2012	2014	2016	2018	2020
CO2 Emissions	338.5	361.5	399.1	422.8	452.1	498.4
Year	2022	2024	2026	2028	2030	2032
CO2 Emissions	559.2	590.9	629.7	663.1	703.1	742.7
(a) Create a linear function that models these data, with x as the number of years past 2010 and y as the millions of metric tons of carbon dioxide emissions. (Round all numerical values to two decimal places.)
y(x) = 
  
Incorrect: Your answer is incorrect.


(b) Find the model's estimate for the 2024 data point. (Round your answer to two decimal places.)
584.42
 
Incorrect: Your answer is incorrect.
 million metric tons

(c) Find the slope of the linear model. (Round your answer to two decimal places.)
19.76
 
Incorrect: Your answer is incorrect.


Interpret the slope of the linear model.
For each year since 
2010
 
Correct: Your answer is correct.
 , carbon dioxide emissions in the U.S. are expected to change by 
19.76
 
Incorrect: Your answer is incorrect.
 million metric tons.

To solve this problem, we need to create a linear function that models the carbon dioxide emissions data. We'll proceed step-by-step to find the correct linear model, verify its accuracy, and answer the related questions.

### (a) Create a Linear Function

Let's assume the linear function has the form:

\[
y(x) = mx + b
\]

where:
- \( y(x) \) represents the millions of metric tons of carbon dioxide emissions.
- \( x \) is the number of years past 2010.
- \( m \) is the slope (rate of change in emissions per year).
- \( b \) is the y-intercept (emissions in 2010).

To find \( m \) and \( b \), we'll use two points from the data. Let's use the first and the last points for simplicity:

1. For the year 2010 (\( x = 0 \)), \( y = 338.5 \)
2. For the year 2032 (\( x = 22 \)), \( y = 742.7 \)

#### Step 1: Calculate the Slope \( m \)

The formula for the slope \( m \) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substitute the values:

\[
m = \frac{742.7 - 338.5}{22 - 0}
\]

Let's calculate the slope.The slope \( m \) is approximately \( 18.37 \) million metric tons per year.

#### Step 2: Calculate the y-intercept \( b \)

Now, we use the slope \( m \) and one of the points to find the y-intercept \( b \). Using the point for the year 2010 (\( x = 0, y = 338.5 \)):

\[
y = mx + b \implies 338.5 = 18.37 \times 0 + b
\]

Since \( x = 0 \), this simplifies to:

\[
b = 338.5
\]

So, the y-intercept \( b \) is \( 338.5 \).

#### Linear Function

Now, we have both the slope and the y-intercept, so the linear function that models the data is:

\[
y(x) = 18.37x + 338.5
\]

### (b) Find the Model's Estimate for the 2024 Data Point

To estimate the data point for the year 2024, we find \( x \) as the number of years past 2010:

\[
x = 2024 - 2010 = 14
\]

Substitute \( x = 14 \) into the linear model:

\[
y(14) = 18.37 \times 14 + 338.5
\]

Let's calculate this value.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can guide you through the steps to find the answer manually.

To find the estimate for the year 2024 using the linear function:

1. **Find \( x \) for the year 2024:**
   \[
   x = 2024 - 2010 = 14
   \]

2. **Substitute \( x = 14 \) into the linear model:**
   \[
   y(14) = 18.37 \times 14 + 338.5
   \]

3. **Calculate:**
   \[
   y(14) = 257.18 + 338.5 = 595.68
   \]

So, the estimated CO₂ emissions for 2024 are approximately **595.68 million metric tons**.

Would you like to proceed with more questions or need further clarification? Here are some related questions to consider:

1. What is the estimated CO₂ emission in 2030 using the same model?
2. How would the linear model change if the emission data were revised?
3. Can a non-linear model better fit the given data?
4. What are the implications of a constant increase in CO₂ emissions for climate policy?
5. How does this data compare to global CO₂ emission trends?

**Tip:** Understanding how to create and interpret linear models is essential for predicting future trends based on current data.

The following table gives the millions of metric tons of carbon dioxide emissions in a certain country for selected years from 2010 and projected to 2032.
Year	2010	2012	2014	2016	2018	2020
CO2 Emissions	338.5	361.5	399.1	422.8	452.1	498.4
Year	2022	2024	2026	2028	2030	2032
CO2 Emissions	559.2	590.9	629.7	663.1	703.1	742.7
(a) Create a linear function that models these data, with x as the number of years past 2010 and y as the millions of metric tons of carbon dioxide emissions. (Round all numerical values to two decimal places.)
y(x) =

(b) Find the model's estimate for the 2024 data point. (Round your answer to two decimal places.)

(c) Find the slope of the linear model. (Round your answer to two decimal places.)

Learn how to model carbon dioxide emissions using a linear function based on data from 2010 to 2032. This step-by-step guide covers creating the linear function, calculating the slope, and estimating future emissions. Suitable for high school students in Grades 10-12.

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