Question

The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $420 to drive 500 mi and in June it cost her $444 to drive 620 mi. (a) Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a suitable model. C(d)

Answer 1

`C(d) = (1)/(5)d + 320`

Explanation:

Given

`d \to miles`

`C \to cost`

So:

`(d_1,C_1) = (500,420)` --- May

`(d_2,C_2) = (620,444)` --- June

Required

Express as a function

Start by calculating the slope (m)

`m = (\triangle C)/(\triangle d)`

`m = (444-420)/(620-500)`

`m = (24)/(120)`

Simplify

`m = (1)/(5)`

The equation is:

`C(d) = m(d - d_1) +C_1`

`C(d) = (1)/(5)(d - 500) +420`

`C(d) = (1)/(5)d - 100 +420`

Take LCM

`C(d) = (1)/(5)d + 320`