Short Answer 
The horsepower function for the race car is defined as H(s) = 0.003s¬≤ + 0.07s – 0.027, where ‘s’ represents speed in mph. After evaluating the function at speeds of 80 and 100 mph, the average rate of change in horsepower is calculated to be 0.61 per unit speed.
Step 1: Define the Function
The horsepower function for the race car is defined as H(s) = 0.003s¬≤ + 0.07s – 0.027. This mathematical relationship shows how horsepower changes with speed. In this case, ‘s’ represents the speed of the car in mph, while ‘H(s)’ shows the corresponding horsepower output at that speed.
Step 2: Calculate Horsepower at Specific Speeds
To find the average rate of change in horsepower, we need to calculate H(80) and H(100). The calculations are as follows:
- For H(80): Substitute s = 80 into the horsepower equation, yielding H(80) = 24.773.
- For H(100): Substitute s = 100 into the equation, resulting in H(100) = 36.973.
Step 3: Compute the Average Rate of Change
Now that we have both horsepower values, we can find the average rate of change using the formula A(s) = (b – a)(H(b) – H(a)), where ‘a’ and ‘b’ are the initial and final speeds respectively.
- Substituting the values gives A(s) = 20(36.973 – 24.773).
- Calculating this difference results in A(s) = 20 x 12.2 = 0.61.
Thus, the average rate of change in horsepower per unit speed is 0.61.