Question

The monthly cost of owning a car depends on the number of kilometers it is driver. Taylor found that in May it cost her $500 to drive 800 km and it June it cost her $650 to drive 1400 km.

1. Express the monthly Cost C as a function of the distance driven d, assuming that a linear function is a suitable model.
2. Use this function to predict the cost of driving 2000 km per month.
3. Find the derivative of the function with appropriate units. What does the derivative of the function represent?
4. Does it cost more to drive the car in December than it does in August? Explain.

Answer 1

in May it cost her $500 to drive 800 km and it June it cost her $650 to drive 1400 km.

two points are

here linear function is a suitable model.

so find slope

.

equation of the line is

......................linear function

.

take x=2000km

it costs $800 to drive 2000 km

.

.

take derivative

here derivative of the function is 0.25. so it costs $0.25 to drive 1 km

.

.

Does it cost more to drive the car in December than it does in August?

it is clearly mentioned that, The monthly cost of owning a car depends on the number of kilometers.

so it does not depend on which month you drive a car