Question

comparing 2 different functions
the function $c(x) = 35x + 75$ represents the labor cost (in dollar) for accurate auto repair shop to replace some major problems with your car, after $x$ hour of work.
your car repairs are estimated to take 6 hours of labor. which company would you go with and why?
accurate auto dunbars auto body
the table below shows the sample labor costs from its main competitor, dunbars auto body.
dunbars auto body

hours	1	2	3

Explanation:

Step1: Find cost for Accurate Auto

Given \( c(x) = 35x + 75 \), for \( x = 6 \):
\( c(6) = 35(6) + 75 = 210 + 75 = 285 \) dollars.

Step2: Find cost function for Dunbar's

From the table, the cost increases by \( 130 - 90 = 40 \) (or \( 170 - 130 = 40 \)) per hour. At \( x = 1 \), cost is 90, so the function is \( d(x) = 40x + 50 \) (check: \( 40(1) + 50 = 90 \), correct). For \( x = 6 \):
\( d(6) = 40(6) + 50 = 240 + 50 = 290 \) dollars.

Step3: Compare costs

Accurate Auto costs $285, Dunbar's costs $290. Since \( 285 < 290 \), Accurate Auto is cheaper.

Answer:

Go with Accurate Auto Repair Shop because its labor cost for 6 hours (\$285) is less than Dunbar’s Auto Body’s cost (\$290) for the same time.