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Gekata [30.6K]
2 years ago
10

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)
Mathematics
1 answer:
djyliett [7]2 years ago
6 0

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

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