Question

My car gets 34 miles per gallon at 60 miles per hour. Is the number of miles I can drive at 60 miles per hour a linear function of the

number of gallons of gas in the tank? Explain your reasoning.
Yes, the number of miles that a car can travel with every gallon of gas is 34, which is constant.
No, the number of miles that a car can travel with every gallon of gas varies, which is not constant.
Identify the growth rate and initial value. (If an answer does not exist, enter DNE.)
Growth rate 34
✓ miles per gallon
Initial value
X miles
Using g for the number of gallons in the tank and M for the number of miles driven, find a formula Mas a linear function of g. (If an
answer does not exist, enter DNE.)
ME

Answer 1

The number of miles driven at 60 mph is a linear function of the gallons of gas in the tank, with a growth rate of 34 miles per gallon and an initial value of 0 miles. The formula for this relationship is M = 34g.

Step-by-step explanation:

Yes, the number of miles that a car can drive at 60 miles per hour is a linear function of the number of gallons of gas in the tank. The reason for this is that the car's fuel efficiency, which is 34 miles per gallon, remains constant when driving at a steady speed of 60 mph. Thus, for every additional gallon of gas in the tank, the car can travel an additional 34 miles.

The growth rate of this function is 34 miles per gallon, because that is the additional distance the car can travel for each additional gallon of gas. The initial value refers to the distance that can be driven with zero gallons of gas, which is obviously zero miles as the car would not move without fuel. This gives an initial value of 0 miles.

Using g for the number of gallons in the tank and M for the number of miles driven, a formula for M as a linear function of g is M = 34g. This represents the linear relationship where M increases by 34 miles for each additional gallon g.