Question

The horsepower, H(s), required for a race car to overcome wind resistance is given by the function H(s)=0.003s²+0.027, where s is the speed of the car in miles per hour. What is the average rate of change in horsepower per unit speed if the racer increases in speed from 80 mph to 100 mph?

Answer 1

The average rate of change in horsepower per unit speed is 0.054 horsepower per mph.

Step-by-step explanation:

The average rate of change in horsepower per unit speed can be found by calculating the difference in horsepower and dividing it by the difference in speed.

Given that the racer increases in speed from 80 mph to 100 mph, the change in speed is 100 - 80 = 20 mph. Substituting this value into the function, we get:

H(100) - H(80) = 0.003(100)^2 + 0.027 - (0.003(80)^2 + 0.027)

H(100) - H(80) = 3 + 0.027 - (1.92 + 0.027) = 3.027 - 1.947 = 1.08

To find the average rate of change, we divide this difference in horsepower by the difference in speed:

Average rate of change = 1.08 / 20 = 0.054 horsepower per mph