FUNCTIONS+CHANGE -WEBASSIGN
6th Edition
ISBN: 9780357422496
Author: Crauder
Publisher: CENGAGE L
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Textbook Question
Chapter 2.6, Problem 10E
Sales Growth In this exercise, we develop a model for the growth rate G, in thousands of dollars per year, in sales of the product as a function of the sales level s, in thousands of dollars. The model assumes that there is a limit to the total amount of sales that can be attained. In this situation, we use the term unattained sales for difference this limit and the current sales level. For example, if we expect sales grow to 3 thousand dollars in the long run, then
a. Find the formula for unattained sales.
b. Write an equation that shows the proportionality relation for G.
c. On the basis of the equation from the part b, make a graph of G as a function of s.
d. At what sales level is the growth rate as large as possible?
e. What is the largest possible growth rate?
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Chapter 2 Solutions
FUNCTIONS+CHANGE -WEBASSIGN
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 - Prob. 15ECh. 2.2 - Monthly Payment for a Home: If you borrow 120,000...Ch. 2.2 - Prob. 17ECh. 2.2 - Alexanders Formula One interesting problem in the...Ch. 2.2 - Prob. 18.2ECh. 2.2 - Prob. 19ECh. 2.2 - Planet Growth The amount of growth of plants in an...Ch. 2.2 - Prob. 21ECh. 2.2 - Viewing Earth: Astronauts looking at Earth from a...Ch. 2.2 - Magazine Circulation: The circulation C of a...Ch. 2.2 - Prob. 24ECh. 2.2 - Buffalo: Waterton Lakes National Park of Canada,...Ch. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 1SBECh. 2.2 - Prob. 2SBECh. 2.2 - Prob. 3SBECh. 2.2 - Prob. 4SBECh. 2.2 - Prob. 5SBECh. 2.2 - Prob. 6SBECh. 2.2 - Prob. 7SBECh. 2.2 - Prob. 8SBECh. 2.2 - Prob. 9SBECh. 2.2 - Prob. 10SBECh. 2.2 - Prob. 11SBECh. 2.2 - Finding Windows and Making Graphs: In Exercises...Ch. 2.2 - Prob. 13SBECh. 2.2 - Prob. 14SBECh. 2.2 - Prob. 15SBECh. 2.2 - Prob. 16SBECh. 2.2 - Prob. 17SBECh. 2.2 - Finding Windows and Making Graphs: In Exercises...Ch. 2.2 - Prob. 19SBECh. 2.2 - Prob. 20SBECh. 2.2 - Prob. 21SBECh. 2.2 - Prob. 22SBECh. 2.2 - Prob. 23SBECh. 2.2 - Prob. 24SBECh. 2.2 - Prob. 25SBECh. 2.2 - Prob. 26SBECh. 2.2 - Prob. 27SBECh. 2.2 - Prob. 28SBECh. 2.2 - Prob. 29SBECh. 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. 3TUCh. 2.3 - Prob. 1ECh. 2.3 - Trans Fat You are ordering fast food for your...Ch. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 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. 13ECh. 2.3 - 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. 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. 30ECh. 2.4 - Home Equity When you purchase a home by securing a...Ch. 2.4 - Prob. 1SBECh. 2.4 - Prob. 2SBECh. 2.4 - Setting Up Equations Each of Exercise S-1 through...Ch. 2.4 - Prob. 4SBECh. 2.4 - Prob. 5SBECh. 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. 8SBECh. 2.4 - Prob. 9SBECh. 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. 12SBECh. 2.4 - Prob. 13SBECh. 2.4 - The Crossing-Graphs Method In Exercise S-5 through...Ch. 2.4 - Prob. 15SBECh. 2.4 - Prob. 16SBECh. 2.4 - Prob. 17SBECh. 2.4 - Prob. 18SBECh. 2.4 - The Single-Graph Method In Exercises S-17 through...Ch. 2.4 - Prob. 20SBECh. 2.4 - Prob. 21SBECh. 2.4 - Prob. 22SBECh. 2.4 - Prob. 23SBECh. 2.4 - Prob. 24SBECh. 2.4 - Prob. 25SBECh. 2.4 - Prob. 26SBECh. 2.4 - The Single-Graph Method In Exercises S-17 through...Ch. 2.4 - Prob. 28SBECh. 2.5 - During what time period would the broker advise...Ch. 2.5 - Prob. 2TUCh. 2.5 - Reminder Round all answers to two decimal places...Ch. 2.5 - Prob. 2ECh. 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. 5.2ECh. 2.5 - Prob. 6ECh. 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. 9ECh. 2.5 - Prob. 10ECh. 2.5 - Reminder Round all answers to two decimal places...Ch. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 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. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - Prob. 1SBECh. 2.5 - Prob. 2SBECh. 2.5 - Finding Inequalities Each of Exercises S-1 through...Ch. 2.5 - Prob. 4SBECh. 2.5 - Solving Inequalities Solve the inequalities in...Ch. 2.5 - Prob. 6SBECh. 2.5 - Prob. 7SBECh. 2.5 - Solving Inequalities Solve the inequalities in...Ch. 2.5 - Prob. 9SBECh. 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. 13SBECh. 2.5 - Prob. 14SBECh. 2.5 - Solving Inequalities Solve the inequalities in...Ch. 2.5 - Prob. 16SBECh. 2.5 - Prob. 17SBECh. 2.5 - Prob. 18SBECh. 2.5 - Prob. 19SBECh. 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. 13ECh. 2.6 - Cost for a Can This is a continuation of Exercises...Ch. 2.6 - Prob. 15ECh. 2.6 - Laying Phone Cable City A lies on the north bank...Ch. 2.6 - Prob. 17ECh. 2.6 - Prob. 18ECh. 2.6 - Prob. 19ECh. 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. 24ECh. 2.6 - Water Flea F. 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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- Flood Control A river is 8 feet above its flood stage. The water is receding at a rate of 3 inches per hour. Write a mathematical model that shows the number of feet above flood stage after t hours. Assuming the water continually recedes at this rate, when will the river be 1 foot above its flood stage?arrow_forwardDuring what time period would the broker advise buying if he thought 500 to 800 was an appropriate buy range? Example 2.10 Beginning in 2001, the price of gold was modeled approximately by G(t)=2551.18t dollars per ounce, where t is the time in years since the beginning of 2001.arrow_forwardGrazing Kangaroos The amount of vegetation eaten in a day by a grazing animal V of food available measured as biomass, in units such as pounds per acre. This relationship is called the functional response. If there is little vegetation available, the daily intake will be small, since the animal will have difficulty finding and eating the food. As the amount of food biomass increases, so does the daily intake. Clearly, though, there is a limit to the amount the animal will eat, regardless of the amount of food available. This maximum amount eaten is the satiation level. a.For the western grey kangaroo of Australia, the functional response is G=2.54.8e0.004V, where G=G(V) is the daily intake measured in pounds and V is the vegetation biomass measured in pounds per acre. i. Draw a graph of G against V. Include vegetation biomass levels up to 2000 pounds per acre. ii. Is the graph you found in part i concave up or concave down? Explain in practical terms what your answer means about how this kangaroo feeds. iii. There is a minimal vegetation biomass level below which the western grey kangaroo will eat nothing. Another way of expressing this is to say that the animal cannot reduce the food biomass below this level. Find this minimal level. iv. Find the satiation level for the western grey kangaroo. b. For the red kangaroo of Australia, the functional response is R=1.91.9e0.033V, Where R is the daily intake measured in pounds and V is the vegetation biomass measured in pounds per acre. i. Add the graph of R against V to the graph of G you drew in part a. ii. A simple measure of the grazing efficiency of an animal involves the minimal vegetation biomass level described above: The lower the minimal level for an animal, the more efficient it is at grazing. Which is more efficient at grazing, the western grey kangaroo or the red kangaroo?arrow_forward
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