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

Answer:

$C(d) = \frac{1}{5}d + 320$

Step-by-step 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)

$m = \frac{\triangle C}{\triangle d}$

$m = \frac{444-420}{620-500}$

$m = \frac{24}{120}$

Simplify

$m = \frac{1}{5}$

The equation is:

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

$C(d) = \frac{1}{5}(d - 500) +420$

$C(d) = \frac{1}{5}d - 100 +420$

Take LCM

$C(d) = \frac{1}{5}d + 320$