The Charges for Renting a Moving Van Are $\$ 65$ For the First 40 Miles And

question 28

Multiple Choice

The charges for renting a moving van are $\$ 65$ for the first 40 miles and $\$ 7$ for each additional mile. Assume that a fraction of a mile is rounded up.
a. Determine the cost of driving the van 98 miles.
b. Find a symbolic representation for a function $\mathrm { f }$ that computes the cost of driving the van $x$ miles, where $0 < x \leq$ (Hint: express f as a piecewise-constant function.)

• A) a. \(\$ 6776\);
• b. \(f ( x ) = \left\{ \begin{array} { l l } 65 & \text { if } 0 < x \leq 40 \\ 65 x + 7 ( x - 40 ) & \text { if } 40 < x \leq 100 \end{array} \right.\)
• B) a. \(\$ 471 ;\)
• b.\(f ( x ) = \left\{ \begin{array} { l l } 65 & \text { if } 0 < x \leq 40 \\ 65 + 7 ( x - 40 ) & \text { if } 40 < x \leq 100 \end{array} \right.\)
• C) a. \(\$ 471 ;\)
• b. \(f ( x ) = \left\{ \begin{array} { l l } 65 & \text { if } 0 < x \leq 40 \\ 65 + 7 ( x + 40 ) & \text { if } 40 < x \leq 100 \end{array} \right.\)
• D) a. \(\$ 1031\);
• b. \(f ( x ) = \left\{ \begin{array} { l l } 65 & \text { if } 0 < x \leq 40 \\ 65 + 7 ( x + 40 ) & \text { if } 40 < x \leq 100 \end{array} \right.\)

---

Definitions:

Leather Shoes

Footwear made from the treated and processed hides of animals, prized for durability, comfort, and style.

Quantity Supplied

The aggregate quantity of a particular good or service that sellers are prepared and able to offer at a certain price point within a given time period.

Quantity Supplied

The overall volume of a specific good or service that producers are eager and able to market at a set price over an established period.

Supply Curve

A graphical representation showing the relationship between the price of a good or service and the quantity supplied for a given period.