a simple model for travel costs involves the cost of gasoline and the cost of a driver. specifically, assume…

a simple model for travel costs involves the cost of gasoline and the cost of a driver. specifically, assume that gasoline costs $p/gallon and the vehicle gets g miles per gallon. also, assume that the driver earns $w/hour. complete parts (a) through (g) below. a. a plausible function to describe how gas mileage (in mi/gal) varies with speed is g(v)=\frac{v(82 - v)}{62}. evaluate g(0), g(40), and g(60) and explain why these values are reasonable. g(0)=□ mpg (round to two decimal places as needed.)

a simple model for travel costs involves the cost of gasoline and the cost of a driver. specifically, assume that gasoline costs $p/gallon and the vehicle gets g miles per gallon. also, assume that the driver earns $w/hour. complete parts (a) through (g) below. a. a plausible function to describe how gas mileage (in mi/gal) varies with speed is g(v)=\frac{v(82 - v)}{62}. evaluate g(0), g(40), and g(60) and explain why these values are reasonable. g(0)=□ mpg (round to two decimal places as needed.)

Answer

Explanation:

Step1: Substitute (v = 0) into (g(v))

[g(0)=\frac{0\times(82 - 0)}{62}] [g(0)=\frac{0\times82}{62}=0]

Step2: Substitute (v = 40) into (g(v))

[g(40)=\frac{40\times(82 - 40)}{62}=\frac{40\times42}{62}=\frac{1680}{62}\approx27.10]

Step3: Substitute (v = 60) into (g(v))

[g(60)=\frac{60\times(82 - 60)}{62}=\frac{60\times22}{62}=\frac{1320}{62}\approx21.29]

The value (g(0) = 0) is reasonable because if the speed (v = 0), the vehicle is not moving, so there is no gas - mileage. The value (g(40)) represents a moderate speed, and a non - zero gas - mileage value is expected. As the speed increases to (v = 60), the gas - mileage (g(60)) is lower than (g(40)) which is consistent with the fact that at higher speeds, a vehicle generally has lower fuel efficiency.

Answer:

(g(0)=0), (g(40)\approx27.10), (g(60)\approx21.29)