Question

The gas tank of a certain car contains 13 gal when the driver of the car begins a trip. For each mile driven by the driver, the amount of gas in the tank decreases by 0.025 gal.

a. Write a linear function for the number of gallons of gas in the tank in terms of the number of miles driven.

b. Use your equation to find the number of gallons in the tank after 180 miles are driven.

Answer 1

The linear function for the number of gallons of gas in the tank is g(m) = 13 - 0.025m. After 180 miles are driven, there will be 8.5 gallons of gas in the tank.

Step-by-step explanation:

To write a linear function for the number of gallons of gas in the tank in terms of the number of miles driven, we can use the formula: gallons = initial gallons - (rate of decrease) * miles driven. In this case, the initial gallons is 13 and the rate of decrease is 0.025 gallons per mile. So the linear function is: g(m) = 13 - 0.025m, where 'm' is the number of miles driven.

To find the number of gallons in the tank after 180 miles are driven, we can substitute 180 for 'm' in the linear function and solve for 'g'. Substituting gives: g(180) = 13 - 0.025(180) = 13 - 4.5 = 8.5. Therefore, there will be 8.5 gallons of gas in the tank after 180 miles are driven.