Question

Is the number of miles a car can drive at 60 miles per hour a linear function of the gallons of gas in the tank?

a. Yes, the number of miles is constant at 34 per gallon.

b. No, the number of miles varies and is not constant.

Identify the growth rate and initial value. (If an answer does not exist, enter DNE.)

a. Growth rate: 34 miles per gallon

b. Initial value: DNE

Using g for the gallons in the tank and M for the miles driven, find a formula ( M ) as a linear function of ( g ).

a. M = 34g

b. M = 60 + 34g

c. M = 34/g

d. M = 60/g

Answer 1

The number of miles a car can drive is a linear function of the gallons of gas in the tank, with a growth rate of 34 miles per gallon and no initial value. The formula representing this linear function is M = 34g.

Step-by-step explanation:

Yes, the number of miles a car can drive at 60 miles per hour is indeed a linear function of the gallons of gas in the tank. This relationship can be represented by a linear equation because for every gallon of gasoline, the car can travel a constant number of miles, assuming we are dealing with average speeds and conditions. If a car travels 34 miles per gallon of gasoline, then the growth rate is 34 miles per gallon, which is the slope of the linear function.

The initial value, in this context, is the number of miles that can be driven without using any gas, which does not exist or is irrelevant; hence, the initial value is Does Not Exist (DNE).

Therefore, the formula for M, the number of miles driven, as a linear function of g, the gallons in the tank, is given by: M = 34g, where M represents the total miles and g represents the gallons of gas in the tank.