Question

1. a car worth $27,500 in 2012 is worth $16,720 in 2016. find the rate of change in the value of the car. 16. the boston red sox had 949 runs in their 2004 season. in their 2015 season, they had 748 runs. find the rate of change in runs. 18. drew measured the snow accumulation during a snowstorm. after the first hour, two inches had accumulated. after six hours, 3 feet had accumulated. find the rate of change.

Explanation:

Question 14

Step1: Identify variables

Let \( x_1 = 2012 \), \( y_1 = 27500 \), \( x_2 = 2016 \), \( y_2 = 16720 \).

Step2: Calculate time difference

\( \Delta x = x_2 - x_1 = 2016 - 2012 = 4 \) years.

Step3: Calculate value difference

\( \Delta y = y_2 - y_1 = 16720 - 27500 = -10780 \) dollars.

Step4: Find rate of change

Rate of change \( = \frac{\Delta y}{\Delta x} = \frac{-10780}{4} = -2695 \) dollars per year.

Step1: Identify variables

Let \( x_1 = 2004 \), \( y_1 = 949 \), \( x_2 = 2015 \), \( y_2 = 748 \).

Step2: Calculate time difference

\( \Delta x = x_2 - x_1 = 2015 - 2004 = 11 \) years.

Step3: Calculate runs difference

\( \Delta y = y_2 - y_1 = 748 - 949 = -201 \) runs.

Step4: Find rate of change

Rate of change \( = \frac{\Delta y}{\Delta x} = \frac{-201}{11} \approx -18.27 \) runs per year.

Step1: Convert units

3 feet = 36 inches (since 1 foot = 12 inches, so \( 3 \times 12 = 36 \) inches).

Step2: Identify variables

Let \( x_1 = 1 \) hour, \( y_1 = 2 \) inches, \( x_2 = 6 \) hours, \( y_2 = 36 \) inches.

Step3: Calculate time difference

\( \Delta x = x_2 - x_1 = 6 - 1 = 5 \) hours.

Step4: Calculate snow difference

\( \Delta y = y_2 - y_1 = 36 - 2 = 34 \) inches.

Step5: Find rate of change

Rate of change \( = \frac{\Delta y}{\Delta x} = \frac{34}{5} = 6.8 \) inches per hour.

Answer:

-2695 dollars per year

Question 16