Chapter 1.4, Problem 19E

Reminder Round all answers to two decimal places unless otherwise indicated.

Renting Motel Rooms You own a motel with $30$ rooms and have a pricing structure that encourages rentals of rooms in groups. One room rents for $\$85.00$, two for $\$83.00$ each, and in general the group rate per room is found by taking $2 off the base of $85 for each extra room rented.

a. How much money do you charge per room if a group rents $3$ rooms? What is the total amount of money you take in?

b. Use a formula to give the rate you charge for each room if you rent $n$ rooms to an organization.

c. Find a formula for a function $R=R\left(n\right)$ that gives the total revenue from renting $n$ rooms to a convention host.

d. Use functional notation to show the total revenue from renting a block of $9$ rooms to a group. Calculate that value.