/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 75 Discounts The manufacturer of a ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q. 75 (page 258)

Discounts The manufacturer of a computer is offering two discounts on last year鈥檚 model computer. The first discount is a $200 rebate and the second discount is 20% off the regular price, p.

(a) Write a function f that represents the sale price if only the rebate applies.

(b) Write a function g that represents the sale price if only the 20% discount applies.

(c) Find f鈭�gand g鈭�f. What does each of these functions represent? Which combination of discounts represents a better deal for the consumer? Why?

Short Answer

Expert verified

(a)fp=p-200

(b)gp=0.8p

(c)f鈭�g=0.8p-200andg鈭�f=0.8p-160

Step by step solution

01

Step 1. Given Information

The manufacturer of a computer is offering two discounts on last year鈥檚 model computer. The first discount is a $200 rebate and the second discount is 20% off the regular price, p.

02

Part (a) Step 1. Finding a function f that represents the sale price if only the rebate applies.

Let p=regular price of the computer

The rebate offered is$200..Thus, the function that will represent the sale price if the rebate$200 is applied is one where is subtracted from the regular price of the computer, that

is:

fp=p-200

03

Part (b) Step 1. A function g that represents the sale price if 20% discount applies

The function that represents the sale price if only the 20%discount is one where 20% is taken off the regular price of the computer.

gp=100-20%pgp=80%p

04

Part (c) Step 1. Finding f∘g

f鈭�g=fgp=f0.8pf鈭�g=0.8p-200

05

Part (c) Step 2. Finding g∘f

g鈭�f=gfx=gfpg鈭�f=gp-200g鈭�f=0.8p-200g鈭�f=0.8p-160

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The hotel Bora-Bora is having a pig roast. At noon, the chef put the pig in a large earthen oven. The pig鈥檚 original temperature was 75掳F. At 2:00 pm the chef checked the pig鈥檚 temperature and was upset because it had reached only 100掳F. If the oven鈥檚 temperature remains a constant 325掳F, at what time may the hotel serve its guests, assuming that pork is done when it reaches 175掳F?

Use transformations to graph the function. Determine the domain, range and horizontal asymptote of the function.

fx=1-2-x/3

In Problems 33-40, the graph of an exponential function is given. Match each graph to one of the following functions.

Population Model The following data represent the population of the United States. An ecologist is interested in building a model that describes the population of the United

States.

(a) Using a graphing utility, draw a scatter diagram of the data using years since 1900 as the independent variable and population as the dependent variable.

(b) Using a graphing utility, build a logistic model from the data.

(c) Using a graphing utility, draw the function found in part (b) on the scatter diagram.

(d) Based on the function found in part (b), what is the carrying capacity of the United States?

(e) Use the function found in part (b) to predict the population of the United States in 2012.

(f) When will the United States population be 350,000,000?

(g) Compare actual U.S. Census figures to the predictions found in parts (e) and (f). Discuss any differences.

Logistic Growth The logistic growth model

P(t)=0.81+1.67e-0.16t

represents the proportion of new cars with a global positioning system (GPS). Let t = 0 represent 2006, t = 1 represent 2007, and so on.

(a) What proportion of new cars in 2006 had a GPS?

(b) Determine the maximum proportion of new cars that have a GPS.

(c) Using a graphing utility, graph P=P(t).

(d) When will 75% of new cars have a GPS?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.