Question

The horsepower , H(s), required for a racecar to overcome wind resistance is given by the function : H(s) = 0.003s^2+0.07s-0.027 , where (s) is the speed of the car in miles per hours. What is the average rate of change in horsepower per unit speed if the race car increases in speed from 80 mph to 100 mph . A 1.64 B. 0.61 C. 12.2 D. 20.0

Answer 1

Average rate of change = [H(100) - H(80)] / (100 - 80)
H(100) = 0.003(100)^2 + 0.07(100) - 0.027 = 0.003(10000) + 0.07(100) - 0.027 = 30 + 7 - 0.027 = 36.973

H(80) = 0.003(80)^2 + 0.07(80) - 0.027 = 0.003(6400) + 0.07(80) - 0.027 = 19.2 + 5.6 - 0.027 = 24.773

Average rate of change = (36.973 - 24.773)/(100 - 80) = 12.2/20 = 0.61

Answer: B

Answer 2

The average rate of change in horsepower per unit speed if the race car increases in speed from 80 mph to 100 mph is 0.61

The function of the horsepower is given as:

$\mathbf{H(s) = 0.003s^2 + 0.07s - 0.027}$

The average rate of change is calculated using:

$\mathbf{A(s) =\frac{H(b) - H(a)}{b - a}}$

Substitute 80 and 100 for a and b, respectively

$\mathbf{A(s) =\frac{H(100) - H(80)}{100 - 80}}$

$\mathbf{A(s) =\frac{H(100) - H(80)}{20}}$

Calculate H(100) and H(80)

$\mathbf{H(80) =0.003 \times 80^2 + 0.07 \times 80 - 0.027 = 24.773}$

$\mathbf{H(100) =0.003 \times 100^2 + 0.07 \times 100 - 0.027 = 36.973}$

So, we have:

$\mathbf{A(s) =\frac{H(100) - H(80)}{20}}$

$\mathbf{A(s) = \frac{36.973 - 24.773}{20}}$

$\mathbf{A(s) = \frac{12.2}{20}}$

$\mathbf{A(s) = 0.61}$

Hence, the average rate of change in horsepower per unit speed is 0.61

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