Problem 1 - Precalculus Essentials

Question

A car rental agency charges \(\$ 200\) per week plus \(\$ 0.15\) per mile to rent a car. a. Express the weekly cost to rent the car, \(f\), as a function of the number of miles driven during the week, \(x\). b. How many miles did you drive during the week if the weekly cost to rent the car was \(\$ 320 ?\)

Step-by-Step Solution

Answer

a) The weekly cost to rent the car, \(f\), as a function of the number of miles driven during the week, \(x\), is \(f(x) = 200 + 0.15x\). b) If the weekly cost to rent the car was $320, then 800 miles were driven during that week.

Step 1: Expressing the cost function

The function \(f(x)\) that represents the weekly cost to rent a car is given as \(f(x) = 200 + 0.15x\), where \(x\) is the number of miles driven.

Step 2: Substituting for Weekly Cost

To find out how many miles you drove if the weekly cost to rent the car was $320, you substitute $320 into the cost function for \(f(x)\). Therefore, the equation becomes: \(320 = 200 + 0.15x\).

Step 3: Solving for \(x\)

To isolate \(x\), subtract 200 from both sides of the equation to get \(120 = 0.15x\). Then divide both sides by 0.15 to solve for \(x\), resulting in \(x = 800\).