Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN: 9781337111348
Author: Bruce Crauder, Benny Evans, Alan Noell
Publisher: Cengage Learning
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Textbook Question
Chapter 2.6, Problem 9E
Forming a pen We want to form a rectangle pen of area 100 square feet. One side of the pen is to be formed by an existing buliding and the other three sides by a fence (see Figure 2.106). Let W be the length, in feet, of the sides of the rectangle perpendicular to the buliding, and let L be the length, in feet, of the other side.
Figure 2.106
a. Find a formula for the total amount of fence needed in terms of W and L
b. Express, as an equation involving W and L, the requirement that the area be 100 square feet.
c. Solve the equation you found in part b for L.
d. Use your answers to parts a and c to find a formula for F, the total amount, in feet, of fence needed, as a function of W alone.
e. Make a graph of F versus W.
f. Determine the dimension of the rectangle that requires a minimum amount of fence.
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Chapter 2 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Ch. 2.1 - If a coffee filter is dropped, its velocity after...Ch. 2.1 - Suppose one canoe rents for 40,and2 is taken off...Ch. 2.1 - A Saving Account You deposit money into a savings...Ch. 2.1 - Savings with regular Deposits Suppose you deposit...Ch. 2.1 - Paying Off a Credit Card Suppose you owe 15, 000...Ch. 2.1 - Buying Power The inflation rate tells us the...Ch. 2.1 - Economic Efficiency Marginal cost is the...Ch. 2.1 - Flesch Reading Ease The Flesch Reading Ease Test...Ch. 2.1 - Spache Readability Formula The Spache Readability...Ch. 2.1 - Weight Lifting Brzyckis formula is used by weight...
Ch. 2.1 - Harvard Step Test The Harvard Step Test was...Ch. 2.1 - Public High School Enrollment One model for the...Ch. 2.1 - Later Public High School Enrollment Here is a...Ch. 2.1 - Species-Area Relation The number of species of...Ch. 2.1 - Competition Two friends enjoy competing with each...Ch. 2.1 - Profit The profit P, in thousands of dollars that...Ch. 2.1 - Prob. 15ECh. 2.1 - Counting when Order Does Not Matter This is a...Ch. 2.1 - APR and EAR Recall that the APR the annual...Ch. 2.1 - An Amortization Table Suppose you borrow P dollars...Ch. 2.1 - Prob. 19ECh. 2.1 - Renting Motel Rooms You own a motel with 30 rooms,...Ch. 2.1 - Prob. 21ECh. 2.1 - A Population of Foxes A breeding group of foxes is...Ch. 2.1 - Falling with a parachute If an average-sized man...Ch. 2.1 - Rolling 4 Sixes If you roll N dice, then the...Ch. 2.1 - Prob. 25ECh. 2.1 - Profit with Varying Price The background for this...Ch. 2.1 - A Precocious Child and Her Blocks A child has 64...Ch. 2.1 - Renting Paddleboats An enterprise rents out...Ch. 2.1 - Growth in Length of Haddock D.S. Raitt found that...Ch. 2.1 - Discharge from a Fire Hose The discharge from a...Ch. 2.1 - Prob. 31ECh. 2.1 - Terminal Velocity Revisited In one of the early...Ch. 2.1 - Research Project Find a function given by formula...Ch. 2.1 - Making Tables and Comparing Functions In Exercises...Ch. 2.1 - Prob. 2SBECh. 2.1 - Prob. 3SBECh. 2.1 - Prob. 4SBECh. 2.1 - Prob. 5SBECh. 2.1 - Prob. 6SBECh. 2.1 - Prob. 7SBECh. 2.1 - Prob. 8SBECh. 2.1 - Prob. 9SBECh. 2.1 - Prob. 10SBECh. 2.1 - Prob. 11SBECh. 2.1 - Finding Limiting Values In Exercises S-11 through...Ch. 2.1 - Prob. 13SBECh. 2.1 - Prob. 14SBECh. 2.1 - Prob. 15SBECh. 2.1 - Prob. 16SBECh. 2.1 - Prob. 17SBECh. 2.1 - Prob. 18SBECh. 2.1 - Prob. 19SBECh. 2.1 - Prob. 20SBECh. 2.1 - Prob. 21SBECh. 2.1 - Prob. 22SBECh. 2.1 - Finding Limiting Values In Exercises S-11 through...Ch. 2.1 - Prob. 24SBECh. 2.1 - Finding Maxima and Minima In Exercises S-25...Ch. 2.1 - Prob. 26SBECh. 2.1 - Prob. 27SBECh. 2.1 - Prob. 28SBECh. 2.1 - Prob. 29SBECh. 2.1 - Prob. 30SBECh. 2.1 - Prob. 31SBECh. 2.1 - Prob. 32SBECh. 2.2 - TEST TOUR UNDERSTANDING FOR EXAMPLE 2.3 Suppose a...Ch. 2.2 - TEST TOUR UNDERSTANDING FOR EXAMPLE 2.4 Changes in...Ch. 2.2 - Continuous Compounding A certain investment is...Ch. 2.2 - Present Value: The present value P is the...Ch. 2.2 - Equity: When you use a mortgage to purchase a...Ch. 2.2 - Buying a Car: If you buy a 25,000 car at an APR of...Ch. 2.2 - Adult Weight from Puppy Weight There is a formula...Ch. 2.2 - Mosteller Formula for Body Surface Area: Body...Ch. 2.2 - Weekly Cost: The weekly cost of running a small...Ch. 2.2 - Average Speed: A commuter regularly drives 70...Ch. 2.2 - Resale Value: The resale value V, in dollars, of a...Ch. 2.2 - Profit The yearly profit P for a widget producer...Ch. 2.2 - Baking a Potato: A potato is placed in a preheated...Ch. 2.2 - Functional Response: The amount C of food consumed...Ch. 2.2 - Population Growth: The growth G of a population...Ch. 2.2 - Ohms Law: says that when electric current is...Ch. 2.2 - 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Sales Strategy A small business is considering...Ch. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - Temperature Conversions In everyday experience,...Ch. 2.3 - The Ideal Gas Law A mole of a chemical is a fixed...Ch. 2.3 - Running Ants A scientist observed that the speed S...Ch. 2.3 - Tax Owed According to the Oklahoma Income Tax...Ch. 2.3 - Prob. 21ECh. 2.3 - Growth in Weight and Height Between the ages of 7...Ch. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Prob. 27ECh. 2.3 - Prob. 1SBECh. 2.3 - Prob. 2SBECh. 2.3 - Prob. 3SBECh. 2.3 - Prob. 4SBECh. 2.3 - Prob. 5SBECh. 2.3 - Prob. 6SBECh. 2.3 - Prob. 7SBECh. 2.3 - Solving Linear Equations In Exercises S-7 through...Ch. 2.3 - Prob. 9SBECh. 2.3 - Solving Linear Equations In Exercises S-7 through...Ch. 2.3 - Prob. 11SBECh. 2.3 - Solving Linear Equations In Exercises S-7 through...Ch. 2.3 - Prob. 13SBECh. 2.3 - Prob. 14SBECh. 2.3 - Prob. 15SBECh. 2.3 - Prob. 16SBECh. 2.3 - Prob. 17SBECh. 2.3 - Prob. 18SBECh. 2.3 - Prob. 19SBECh. 2.3 - Prob. 20SBECh. 2.3 - Prob. 21SBECh. 2.3 - Prob. 22SBECh. 2.3 - Prob. 23SBECh. 2.3 - Prob. 24SBECh. 2.3 - Prob. 25SBECh. 2.3 - Prob. 26SBECh. 2.3 - Prob. 27SBECh. 2.3 - Reversing Roles of Variables In Exercises S-17...Ch. 2.3 - Prob. 29SBECh. 2.3 - Prob. 30SBECh. 2.4 - The number N of deer expected to be present on the...Ch. 2.4 - Prob. 2TUCh. 2.4 - Doubling Time An investment grows according to the...Ch. 2.4 - You Win the Lottery Congratulations You have just...Ch. 2.4 - Prob. 3ECh. 2.4 - Your Childs Education You want to begin making...Ch. 2.4 - Engine Displacement The displacement for an...Ch. 2.4 - Altmans z-score Altmans z-score is a financial...Ch. 2.4 - Admiralty Coefficient The Admiralty Coefficent A...Ch. 2.4 - Properller Size An ideal diameter d, in feet, of a...Ch. 2.4 - A Population of Foxes A breeding group of foxes is...Ch. 2.4 - Profit The monthly profit P for a widget producer...Ch. 2.4 - Prob. 11ECh. 2.4 - The Skydiver Again When a skydiver jumps from an...Ch. 2.4 - Falling with a Parachute If an average-sized man...Ch. 2.4 - A Cup of Cofee The temperature C of a fresh cup of...Ch. 2.4 - Reaction Rates In a chemical reaction, the...Ch. 2.4 - Population Growth The growth G of a population of...Ch. 2.4 - Van der Waals Equation In Exercise 18 at the end...Ch. 2.4 - Radioactive Decay The half-life of a radioactive...Ch. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Grazing Kangaroos The amount of vegetation eaten...Ch. 2.4 - Grazing Rabbits and Sheep This is a continuation...Ch. 2.4 - Prob. 23ECh. 2.4 - Hosting a Convention You are hosting a convention...Ch. 2.4 - Breaking Even The background for this exercise can...Ch. 2.4 - Prob. 26ECh. 2.4 - Water Flea F. 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E. Smith has studied population...Ch. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Maximum and Minimum Values In Exercise S-1 through...Ch. 2.6 - Maximum and Minimum Values In Exercise S-1 through...Ch. 2.6 - Prob. 3SBECh. 2.6 - Prob. 4SBECh. 2.6 - Prob. 5SBECh. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Prob. 8SBECh. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Prob. 10SBECh. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Prob. 12SBECh. 2.6 - Prob. 13SBECh. 2.6 - Prob. 14SBECh. 2.6 - Prob. 15SBECh. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Prob. 17SBECh. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Prob. 20SBECh. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Prob. 22SBECh. 2.6 - Prob. 23SBECh. 2.6 - Prob. 24SBECh. 2.6 - Prob. 25SBECh. 2.6 - Prob. 26SBECh. 2.6 - Endpoint Maximum Find the maximum value of...Ch. 2.6 - Maximum and Minimum Find the maximum and minimum...Ch. 2.CR - Finding a Minimum Suppose the function...Ch. 2.CR - Population of Foxes A breeding group of foxes is...Ch. 2.CR - Prob. 3CRCh. 2.CR - Water Jug If a completely full 5-gallon water jug...Ch. 2.CR - Maxima and Minima Find the maximum and minimum...Ch. 2.CR - George Reserve Population The number of deer on...Ch. 2.CR - Prob. 7CRCh. 2.CR - Forming a Pen We want to form a free-standing...Ch. 2.CR - The Crossing-Graphs Method Solve using the...Ch. 2.CR - Prob. 10CRCh. 2.CR - Prob. 11CRCh. 2.CR - Prob. 12CRCh. 2.CR - Linear Equations Solve for W:L=98.42+1.08W4.14A.Ch. 2.CR - Growth of North Sea Sole The length of North Sea...Ch. 2.CR - Minimum Find the minimum value of x2+20/(x+1) on...Ch. 2.CR - Prob. 16CRCh. 2.CR - Prob. 17CRCh. 2.CR - Temperature Conversions The three principal...Ch. 2.CR - Lidocaine Lidocaine is a drug used to treat...Ch. 2.CR - The Single-Graph Method Use the single-graph...Ch. 2.CR - Prob. 21CRCh. 2.FR1 - Prob. 1ECh. 2.FR1 - Prob. 2ECh. 2.FR1 - Prob. 3ECh. 2.FR1 - Prob. 4ECh. 2.FR1 - Prob. 5ECh. 2.FR1 - Prob. 6ECh. 2.FR1 - Prob. 7ECh. 2.FR1 - Prob. 8ECh. 2.FR1 - Prob. 9ECh. 2.FR1 - Prob. 10ECh. 2.FR1 - Prob. 11ECh. 2.FR1 - Prob. 12ECh. 2.FR1 - Prob. 13ECh. 2.FR1 - Prob. 14ECh. 2.FR1 - Prob. 15ECh. 2.FR2 - Prob. 1ECh. 2.FR2 - Prob. 2ECh. 2.FR2 - Prob. 3ECh. 2.FR2 - Prob. 4ECh. 2.FR2 - Prob. 5ECh. 2.FR2 - Prob. 6ECh. 2.FR2 - Prob. 7ECh. 2.FR2 - Prob. 8ECh. 2.FR2 - Prob. 9ECh. 2.FR2 - Prob. 10ECh. 2.FR2 - Prob. 11ECh. 2.FR2 - Prob. 12ECh. 2.FR2 - Prob. 13ECh. 2.FR2 - Prob. 14ECh. 2.FR2 - Prob. 15ECh. 2.FR3 - Locating the Vertex of a Parabola In Exercises 1...Ch. 2.FR3 - Prob. 2ECh. 2.FR3 - Prob. 3ECh. 2.FR3 - Prob. 4ECh. 2.FR3 - Prob. 5ECh. 2.FR3 - Prob. 6ECh. 2.FR3 - Applications Exercises 5 through 13 illustrate...Ch. 2.FR3 - Prob. 8ECh. 2.FR3 - Prob. 9ECh. 2.FR3 - Prob. 10ECh. 2.FR3 - Prob. 11ECh. 2.FR3 - Prob. 12ECh. 2.FR3 - Prob. 13E
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