Question

Question was provided via image upload.

Explanation:

Part 1: Identifying Variables

• The independent variable \( x \) represents the number of hours since snow began falling (because it's the variable we can control or that changes independently).
• The dependent variable is the total amount of snow on the lawn (because the amount of snow depends on how many hours it has been snowing).

Part 2: Function Definition

Step 1: Determine the initial amount and rate

The initial amount of snow is 10 inches, and the rate of snowfall is 2 inches per hour. The total amount of snow \( D(x) \) (in inches) after \( x \) hours is the initial amount plus the amount of snow that falls in \( x \) hours. The amount of snow that falls in \( x \) hours is \( 2x \) (since it's 2 inches per hour for \( x \) hours).
So the function is \( D(x)=10 + 2x \).

Step 3: Calculate \( D(9) \)

To find \( D(9) \), we substitute \( x = 9 \) into the function \( D(x)=10+2x \).
\( D(9)=10 + 2\times9 \)
First, calculate \( 2\times9 = 18 \).
Then, \( 10+18 = 28 \).

Final Answers:

• Independent variable \( x \): number of hours since snow began falling
• Dependent variable: total amount of snow on the lawn (because the total amount of snow depends on the number of hours since snow began falling)
• Function: \( D(x)=\boldsymbol{10 + 2x} \)
• \( D(9)=\boldsymbol{28} \) (meaning after 9 hours, the total amount of snow on the lawn is 28 inches)

Answer:

Part 1: Identifying Variables

• The independent variable \( x \) represents the number of hours since snow began falling (because it's the variable we can control or that changes independently).
• The dependent variable is the total amount of snow on the lawn (because the amount of snow depends on how many hours it has been snowing).

Part 2: Function Definition

Step 1: Determine the initial amount and rate

The initial amount of snow is 10 inches, and the rate of snowfall is 2 inches per hour. The total amount of snow \( D(x) \) (in inches) after \( x \) hours is the initial amount plus the amount of snow that falls in \( x \) hours. The amount of snow that falls in \( x \) hours is \( 2x \) (since it's 2 inches per hour for \( x \) hours).
So the function is \( D(x)=10 + 2x \).

Step 3: Calculate \( D(9) \)

To find \( D(9) \), we substitute \( x = 9 \) into the function \( D(x)=10+2x \).
\( D(9)=10 + 2\times9 \)
First, calculate \( 2\times9 = 18 \).
Then, \( 10+18 = 28 \).

Final Answers:

• Independent variable \( x \): number of hours since snow began falling
• Dependent variable: total amount of snow on the lawn (because the total amount of snow depends on the number of hours since snow began falling)
• Function: \( D(x)=\boldsymbol{10 + 2x} \)
• \( D(9)=\boldsymbol{28} \) (meaning after 9 hours, the total amount of snow on the lawn is 28 inches)