cost to own and operate a car depends on many factors, including gas prices, insurance costs, size of car, and finance charges. Using a cost calculator found on the Internet, the owner determined it costs him approximately $0.685 pe-
to own and operate a car. The total cost is a function of the number of miles driven and can be represented by the function C = 0.685m. When the owner finally takes his car to the junkyard, the odometer reads 158,200 miles. Complete
is a through f.
a) Find the total cost to own and operate the car for the entire time the owner had it.
To find the total cost, we can plug in the number of miles driven into the cost function:
C = 0.685 * 158,200
C = 108,493
Therefore, the total cost to own and operate the car for the entire time is $108,493.
b) Find the average cost per mile to own and operate the car.
To find the average cost per mile, we divide the total cost by the number of miles driven:
average cost per mile = total cost / number of miles
average cost per mile = 108,493 / 158,200
average cost per mile ≈ $0.685
Therefore, the average cost per mile to own and operate the car is approximately $0.685.
c) If the owner was to buy a new car, how many miles would he need to drive in order for the cost to be equal to the total cost of owning and operating the car he just junked?
Let x be the number of miles the owner would need to drive in order for the cost to be equal to the total cost of owning and operating the car he just junked. The cost function for the new car would be:
C_new = 0.685x
Since this cost has to be equal to $108,493, we set up the equation:
0.685x = 108,493
x = 158,518 miles
Therefore, the owner would need to drive 158,518 miles in the new car for the cost to be equal to the total cost of owning and operating the car he just junked.
d) If gas prices increase by 20%, how does that affect the cost of owning and operating the car?
If gas prices increase by 20%, the cost per mile would increase by 20% as well. The new cost per mile would be:
New cost per mile = $0.685 * 1.20
New cost per mile = $0.822
Therefore, with gas prices increasing by 20%, the cost of owning and operating the car would increase to $0.822 per mile.
e) If insurance costs decrease by 10%, how does that affect the cost of owning and operating the car?
If insurance costs decrease by 10%, the total cost to own and operate the car would decrease as well. However, without knowing the exact percentage of insurance costs in the total cost, it is difficult to calculate the exact impact on the total cost.
f) If the owner finances the car with a loan that charges 5% interest, how does that affect the total cost of owning and operating the car?
If the owner finances the car with a loan that charges 5% interest, the total cost of owning and operating the car would increase due to the added finance charges. It would be important to factor in the total amount financed and the length of the loan to accurately calculate the impact on the total cost.