Math

QuestionWhat does the slope of the function C=(0.05+0.14)x+1,000C=(0.05+0.14)x+1,000 represent regarding car ownership costs? A) Insurance cost B) Fuel and insurance cost C) Cost per mile D) Maintenance and fuel cost per mile

Studdy Solution

STEP 1

Assumptions1. The cost of maintenance is5 cents per mile. The cost of fuel is14 cents per mile3. The cost of insurance is 1,000peryear4.Theequation1,000 per year4. The equation C=(0.05+0.14) x+1,000representsthetotalcostofowningandoperatingthecarforayear,where represents the total cost of owning and operating the car for a year, where Cisthetotalcostand is the total cost and x$ is the number of miles driven in a year

STEP 2

The equation given is in the form of a linear equation y=mx+by=mx+b, where mm is the slope and bb is the y-intercept. In this case, CC is equivalent to yy, xx is equivalent to xx, (0.05+0.14)(0.05+0.14) is equivalent to mm, and 1,0001,000 is equivalent to bb.

STEP 3

The slope of a function in a linear equation represents the rate of change of the dependent variable (CC in this case) with respect to the independent variable (xx in this case).

STEP 4

In the context of this problem, the slope (0.05+0.14)(0.05+0.14) represents the rate of change of the total cost of owning and operating the car with respect to the number of miles driven in a year.

STEP 5

The slope is the sum of the costs of maintenance and fuel per mile, which is (0.05+0.14)(0.05+0.14) dollars per mile.

STEP 6

Therefore, the slope of the graph of this function represents the cost of maintenance and fuel per mile.
The correct answer is D) The cost of maintenance and fuel per mile.

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