Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

The Elite Limo company charges by the hour for use of its cars. The charge for the first hour or part is $\$ 80 .$ The charge for each additional hour or part up to 6 hours is $\$ 55,$ and for each hour or part above 6 hours the hourly charge is \$48. (a) Determine $C(h)$ an equation represent the cost $C$ of the ride in terms of the hours $h$. What is the charge for (b) 4 hours, (c) 7 hours.

(a) $C(h)=\left\{\begin{array}{cc}80 & h<1 \\ 25+55 h & 1 \leq h<6 \\ 67+48 h & h \geq 6\end{array}\right.$(b) $\$ 245$(c) $\$ 403$

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

Missouri State University

Campbell University

Harvey Mudd College

Idaho State University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

03:18

00:33

The cost, $\$ C$, of renti…

00:46

The B737-400 aircraft cost…

02:52

GRIDDABLE The cost to park…

01:32

The cost per hour for fuel…

03:24

Several equipment rental s…

01:04

A plumber charges $$\$ 50$…

07:33

[T] A rental car company r…

01:21

A group of college student…

01:05

Suppose that bike rentals …

01:11

The pricing schedule for l…

01:10

A studio engineer charges …

01:13

this problem outlines the charges from the elite limo company. If you want to rent one of their cars, our goal is to figure out a function that represents the costs. See, in terms of the number of hours h that somebody wants to rent the car. For now, we have three distinct cases, so I'm going to write this in a piece. Wise function, with three parts at the first part is the easiest. If you rent it for an hour or less, it's $80. Nothing to figure out up to an hour. It's $80. Well, the next group is. What if it's under six? That means that it's more than one hour, but less than or equal to six. Well, in that case, the first hour is still $80 but every other hour that's H minus. One hours costs $55. So, for example, if I had it out for three hours, that means I have one hour at 88 at $80 and the other two at 55. Now what if H is more than six hours? Well, let's take a moment and see how much it costs for those first six hours. Let's let's take a look at our function and let H equal six. That would be $80 for the first hour and then five hours at $55 apiece. That gives me a total of $355. So if I rent this for over six hours, I know the first six they're gonna cost me 355. All of the rest of the hours are going to cost $48 and that's going to be a change minus six. For example, let's say I rented for eight hours. The first six hours are covered in that $355. H minus six would be eight minus six or two. I have two additional hours at that bigger cost. So there is my piece wise function. Now there's another way we can write this. You only have to show one of thes, but I'm gonna write both of them just so you can see, um, they are exactly the same. Just a different way of writing it, and that is to write it with no parentheses. I'm still gonna have 80 for less than one hour, but If I use the distributive property, get rid of those parentheses. Add everything up together. That gives me 25 plus 55 h for that second case. It's the same numbers. I've just got rid of the parentheses. You would probably have to write that this one first. But if you like it without the parentheses, you can always change it. And let's do the last one. If I get rid of those parentheses and put everything together, that gives me 67 plus 48 h. Okay, so that's what we have. They they're identical math wise. It's just a different way of writing it. Okay, now let's use thes, and it doesn't matter which one we use. I'll use the second one here when we go to put our numbers in. Let's see how much is going to cost us in two cases. First four hours. Well, four hours is going to be case number two, that second one, because this between one and six hours. So I'll have $25 plus 55 times four, and when you do that out, you get a value of $245 that is going to cost. What if we have it longer? What if C equals R H equals 77 hours? Well, now we're in our third case. That's more than six. So I have 67 plus 48 times seven, and that's going to give me a grand total off $403 to rent the limo.

View More Answers From This Book

Find Another Textbook

01:06

You are given a pair of equations, one representing a supply curve and the o…

02:29

Let $y=f(x)$ describe the upper half of the circle $x^{2}+y^{2}=16 .$ Determ…

02:21

Find the slope of the line passing through each pair of points.$$(1 / 2,…

03:12

(a) determine the domain, (b) sketch the graph and (c) determine the range o…

01:29

Determine the horizontal asymptotes, if they exists.$$f(x)=\frac{(2 x-1)…

03:30

Determine the center and radius of the given circle and sketch its graph.

03:19

sketch the graph of the given ellipse, labeling all intercepts.$$4 x^{2}…

03:52

Find the indicated limit.$$\lim _{h \rightarrow 0} \frac{(x+2 h)^{2}-x^{…

02:40

Discuss the continuity of the function defined by $f(x)=\frac{x^{2}-9}{x-3}$…

03:03

Determine the derivative at the given point on the curve using equation (2).…