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Math Algebra FUNCTIONS AND CHANGE COMBO

Size of High Schools The farm population has declined dramatically in the years since World War II, and with that decline, rural school districts have been faced with consolidating in order to be economically efficient. One researcher studied data from the early 1960s on expenditures for high schools ranging from 150 to 2400 in enrollment. He considered the cost per pupil as a function of the number of pupils enrolled in the high school, and he found the approximate formula C = 743 − 0.402 n + 0.00012 n 2 where n is the number of pupils enrolled and C is the cost, in dollars, per pupil. a . Make a graph of C versus n . b . What enrollment size gives a minimum per-pupil cost? c . If a high school had an enrollment of 1200, how much in per-pupil cost would be saved by increasing enrollment to the optimal size found in part b?

Size of High Schools The farm population has declined dramatically in the years since World War II, and with that decline, rural school districts have been faced with consolidating in order to be economically efficient. One researcher studied data from the early 1960s on expenditures for high schools ranging from 150 to 2400 in enrollment. He considered the cost per pupil as a function of the number of pupils enrolled in the high school, and he found the approximate formula C = 743 − 0.402 n + 0.00012 n 2 where n is the number of pupils enrolled and C is the cost, in dollars, per pupil. a . Make a graph of C versus n . b . What enrollment size gives a minimum per-pupil cost? c . If a high school had an enrollment of 1200, how much in per-pupil cost would be saved by increasing enrollment to the optimal size found in part b?

Solution Summary: The author analyzes the cost per pupil as a function of the number of pupils enrolled in the high school.

FUNCTIONS AND CHANGE COMBO

FUNCTIONS AND CHANGE COMBO

6th Edition

ISBN: 9781337801287

Author: Crauder

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Textbook Question

Chapter 2.6, Problem 23E

Size of High Schools The farm population has declined dramatically in the years since World War II, and with that decline, rural school districts have been faced with consolidating in order to be economically efficient. One researcher studied data from the early 1960s on expenditures for high schools ranging from 150 to 2400 in enrollment. He considered the cost per pupil as a function of the number of pupils enrolled in the high school, and he found the approximate formula

C = 743 − 0.402 n + 0.00012 n 2

where n is the number of pupils enrolled and C is the cost, in dollars, per pupil.

a. Make a graph of C versus n.

b. What enrollment size gives a minimum per-pupil cost?

c. If a high school had an enrollment of 1200, how much in per-pupil cost would be saved by increasing enrollment to the optimal size found in part b?

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Chapter 2.6, Problem 22E

Chapter 2.6, Problem 24E

Chapter 2 Solutions

FUNCTIONS AND CHANGE COMBO

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Prob. 20SBE Ch. 2.2 - Prob. 21SBE Ch. 2.2 - Prob. 22SBE Ch. 2.2 - Prob. 23SBE Ch. 2.2 - Prob. 24SBE Ch. 2.2 - Prob. 25SBE Ch. 2.2 - Prob. 26SBE Ch. 2.2 - Prob. 27SBE Ch. 2.2 - Prob. 28SBE Ch. 2.2 - Prob. 29SBE Ch. 2.2 - Finding Windows and Making Graphs: In Exercises...Ch. 2.3 - In the situation of the example, how long could...Ch. 2.3 - If you travel 300 miles on the first day and then...Ch. 2.3 - Prob. 3TU Ch. 2.3 - Prob. 1E Ch. 2.3 - Trans Fat You are ordering fast food for your...Ch. 2.3 - Prob. 3E Ch. 2.3 - Prob. 4E Ch. 2.3 - Break-even Point A manufacturer of T-shirts has...Ch. 2.3 - Juice Sales The number J, in thousands, of cans of...Ch. 2.3 - Resale Value The resale value V, in thousands of...Ch. 2.3 - Aerobic Power Aerobic power can be thought of as...Ch. 2.3 - Gas Mileage The distance d, in miles, that you can...Ch. 2.3 - Isocost Equation We are to buy quantities of two...Ch. 2.3 - Supply and Demand The quantity S of barley, in...Ch. 2.3 - Stock Turnover at Retail In retail sales, an...Ch. 2.3 - Prob. 13E Ch. 2.3 - Sales Strategy A small business is considering...Ch. 2.3 - Prob. 15E Ch. 2.3 - Prob. 16E Ch. 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. 21E Ch. 2.3 - Growth in Weight and Height Between the ages of 7...Ch. 2.3 - Prob. 23E Ch. 2.3 - Prob. 24E Ch. 2.3 - Prob. 25E Ch. 2.3 - Prob. 26E Ch. 2.3 - Prob. 27E Ch. 2.3 - Prob. 1SBE Ch. 2.3 - Prob. 2SBE Ch. 2.3 - Prob. 3SBE Ch. 2.3 - Prob. 4SBE Ch. 2.3 - Prob. 5SBE Ch. 2.3 - Prob. 6SBE Ch. 2.3 - Prob. 7SBE Ch. 2.3 - Solving Linear Equations In Exercises S-7 through...Ch. 2.3 - Prob. 9SBE Ch. 2.3 - Solving Linear Equations In Exercises S-7 through...Ch. 2.3 - Prob. 11SBE Ch. 2.3 - Solving Linear Equations In Exercises S-7 through...Ch. 2.3 - Prob. 13SBE Ch. 2.3 - Prob. 14SBE Ch. 2.3 - Prob. 15SBE Ch. 2.3 - Prob. 16SBE Ch. 2.3 - Prob. 17SBE Ch. 2.3 - Prob. 18SBE Ch. 2.3 - Prob. 19SBE Ch. 2.3 - Prob. 20SBE Ch. 2.3 - Prob. 21SBE Ch. 2.3 - Prob. 22SBE Ch. 2.3 - Prob. 23SBE Ch. 2.3 - Prob. 24SBE Ch. 2.3 - Prob. 25SBE Ch. 2.3 - Prob. 26SBE Ch. 2.3 - Prob. 27SBE Ch. 2.3 - Reversing Roles of Variables In Exercises S-17...Ch. 2.3 - Prob. 29SBE Ch. 2.3 - Prob. 30SBE Ch. 2.4 - The number N of deer expected to be present on the...Ch. 2.4 - Prob. 2TU Ch. 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. 3E Ch. 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. 11E Ch. 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. 19E Ch. 2.4 - Prob. 20E Ch. 2.4 - Grazing Kangaroos The amount of vegetation eaten...Ch. 2.4 - Grazing Rabbits and Sheep This is a continuation...Ch. 2.4 - Prob. 23E Ch. 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. 26E Ch. 2.4 - Water Flea F. E Smith has reported on population...Ch. 2.4 - Hollings Functional Response Curve The total...Ch. 2.4 - Radius of a Shock Wave An explosion produces a...Ch. 2.4 - Prob. 30E Ch. 2.4 - Home Equity When you purchase a home by securing a...Ch. 2.4 - Prob. 1SBE Ch. 2.4 - Prob. 2SBE Ch. 2.4 - Setting Up Equations Each of Exercise S-1 through...Ch. 2.4 - Prob. 4SBE Ch. 2.4 - Prob. 5SBE Ch. 2.4 - The Crossing-Graphs Method In Exercise S-5 through...Ch. 2.4 - The Crossing-Graphs Method In Exercise S-5 through...Ch. 2.4 - Prob. 8SBE Ch. 2.4 - Prob. 9SBE Ch. 2.4 - The Crossing-Graphs Method In Exercise S-5 through...Ch. 2.4 - The Crossing-Graphs Method In Exercise S-5 through...Ch. 2.4 - Prob. 12SBE Ch. 2.4 - Prob. 13SBE Ch. 2.4 - The Crossing-Graphs Method In Exercise S-5 through...Ch. 2.4 - Prob. 15SBE Ch. 2.4 - Prob. 16SBE Ch. 2.4 - Prob. 17SBE Ch. 2.4 - Prob. 18SBE Ch. 2.4 - The Single-Graph Method In Exercises S-17 through...Ch. 2.4 - Prob. 20SBE Ch. 2.4 - Prob. 21SBE Ch. 2.4 - Prob. 22SBE Ch. 2.4 - Prob. 23SBE Ch. 2.4 - Prob. 24SBE Ch. 2.4 - Prob. 25SBE Ch. 2.4 - Prob. 26SBE Ch. 2.4 - The Single-Graph Method In Exercises S-17 through...Ch. 2.4 - Prob. 28SBE Ch. 2.5 - During what time period would the broker advise...Ch. 2.5 - Prob. 2TU Ch. 2.5 - Reminder Round all answers to two decimal places...Ch. 2.5 - Prob. 2E Ch. 2.5 - Reminder Round all answers to two decimal places...Ch. 2.5 - Reminder Round all answers to two decimal places...Ch. 2.5 - Reminder Round all answers to two decimal places...Ch. 2.5 - Prob. 5.2E Ch. 2.5 - Prob. 6E Ch. 2.5 - Reminder Round all answers to two decimal places...Ch. 2.5 - Reminder Round all answers to two decimal places...Ch. 2.5 - Prob. 9E Ch. 2.5 - Prob. 10E Ch. 2.5 - Reminder Round all answers to two decimal places...Ch. 2.5 - Prob. 12E Ch. 2.5 - Prob. 13E Ch. 2.5 - Prob. 14E Ch. 2.5 - Reminder Round all answers to two decimal places...Ch. 2.5 - Reminder Round all answers to two decimal places...Ch. 2.5 - Prob. 17E Ch. 2.5 - Prob. 18E Ch. 2.5 - Prob. 19E Ch. 2.5 - Prob. 20E Ch. 2.5 - Prob. 21E Ch. 2.5 - Prob. 1SBE Ch. 2.5 - Prob. 2SBE Ch. 2.5 - Finding Inequalities Each of Exercises S-1 through...Ch. 2.5 - Prob. 4SBE Ch. 2.5 - Solving Inequalities Solve the inequalities in...Ch. 2.5 - Prob. 6SBE Ch. 2.5 - Prob. 7SBE Ch. 2.5 - Solving Inequalities Solve the inequalities in...Ch. 2.5 - Prob. 9SBE Ch. 2.5 - Solving Inequalities Solve the inequalities in...Ch. 2.5 - Solving Inequalities Solve the inequalities in...Ch. 2.5 - Solving Inequalities Solve the inequalities in...Ch. 2.5 - Prob. 13SBE Ch. 2.5 - Prob. 14SBE Ch. 2.5 - Solving Inequalities Solve the inequalities in...Ch. 2.5 - Prob. 16SBE Ch. 2.5 - Prob. 17SBE Ch. 2.5 - Prob. 18SBE Ch. 2.5 - Prob. 19SBE Ch. 2.6 - TEST YOUR UNTERSTANDING FOR EXAMPLE 2.12 Replace...Ch. 2.6 - World Crude Oil Production In 1956, M.King Hubbert...Ch. 2.6 - Life Expectancy Versus Health Care Spending One...Ch. 2.6 - Builders Old Measurement The Builders Old...Ch. 2.6 - Drug Concentration When a drug is administered...Ch. 2.6 - The Cannon at a Different Angle Suppose a cannon...Ch. 2.6 - Profit The weekly profit P for a widget producer...Ch. 2.6 - Marine Fishery One class of models for population...Ch. 2.6 - Enclosing a field You have 16 miles of fence that...Ch. 2.6 - Forming a pen We want to form a rectangle pen of...Ch. 2.6 - Sales Growth In this exercise, we develop a model...Ch. 2.6 - Maximum Sales Growth This is a continuation of...Ch. 2.6 - An Aluminum Can The cost of making a can is...Ch. 2.6 - Prob. 13E Ch. 2.6 - Cost for a Can This is a continuation of Exercises...Ch. 2.6 - Prob. 15E Ch. 2.6 - Laying Phone Cable City A lies on the north bank...Ch. 2.6 - Prob. 17E Ch. 2.6 - Prob. 18E Ch. 2.6 - Prob. 19E Ch. 2.6 - Spawner-Recruit Model In fish management it is...Ch. 2.6 - Rate of Growth The rate of growth G in the weight...Ch. 2.6 - Health Plan The manager of an employee health plan...Ch. 2.6 - Size of High Schools The farm population has...Ch. 2.6 - Prob. 24E Ch. 2.6 - Water Flea F. E. Smith has studied population...Ch. 2.6 - Prob. 26E Ch. 2.6 - Prob. 27E Ch. 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. 3SBE Ch. 2.6 - Prob. 4SBE Ch. 2.6 - Prob. 5SBE Ch. 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. 8SBE Ch. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Prob. 10SBE Ch. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Prob. 12SBE Ch. 2.6 - Prob. 13SBE Ch. 2.6 - Prob. 14SBE Ch. 2.6 - Prob. 15SBE Ch. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Prob. 17SBE Ch. 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. 20SBE Ch. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Prob. 22SBE Ch. 2.6 - Prob. 23SBE Ch. 2.6 - Prob. 24SBE Ch. 2.6 - Prob. 25SBE Ch. 2.6 - Prob. 26SBE Ch. 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. 3CR Ch. 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. 7CR Ch. 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. 10CR Ch. 2.CR - Prob. 11CR Ch. 2.CR - Prob. 12CR Ch. 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. 16CR Ch. 2.CR - Prob. 17CR Ch. 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. 21CR Ch. 2.FR1 - Prob. 1E Ch. 2.FR1 - Prob. 2E Ch. 2.FR1 - Prob. 3E Ch. 2.FR1 - Prob. 4E Ch. 2.FR1 - Prob. 5E Ch. 2.FR1 - Prob. 6E Ch. 2.FR1 - Prob. 7E Ch. 2.FR1 - Prob. 8E Ch. 2.FR1 - Prob. 9E Ch. 2.FR1 - Prob. 10E Ch. 2.FR1 - Prob. 11E Ch. 2.FR1 - Prob. 12E Ch. 2.FR1 - Prob. 13E Ch. 2.FR1 - Prob. 14E Ch. 2.FR1 - Prob. 15E Ch. 2.FR2 - Prob. 1E Ch. 2.FR2 - Prob. 2E Ch. 2.FR2 - Prob. 3E Ch. 2.FR2 - Prob. 4E Ch. 2.FR2 - Prob. 5E Ch. 2.FR2 - Prob. 6E Ch. 2.FR2 - Prob. 7E Ch. 2.FR2 - Prob. 8E Ch. 2.FR2 - Prob. 9E Ch. 2.FR2 - Prob. 10E Ch. 2.FR2 - Prob. 11E Ch. 2.FR2 - Prob. 12E Ch. 2.FR2 - Prob. 13E Ch. 2.FR2 - Prob. 14E Ch. 2.FR2 - Prob. 15E Ch. 2.FR3 - Locating the Vertex of a Parabola In Exercises 1...Ch. 2.FR3 - Prob. 2E Ch. 2.FR3 - Prob. 3E Ch. 2.FR3 - Prob. 4E Ch. 2.FR3 - Prob. 5E Ch. 2.FR3 - Prob. 6E Ch. 2.FR3 - Applications Exercises 5 through 13 illustrate...Ch. 2.FR3 - Prob. 8E Ch. 2.FR3 - Prob. 9E Ch. 2.FR3 - Prob. 10E Ch. 2.FR3 - Prob. 11E Ch. 2.FR3 - Prob. 12E Ch. 2.FR3 - Prob. 13E

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