Math

CalculusApplied Calculus for the Managerial, Life, and Social Sciences: A Brief ApproachPredator-Prey Model The relationship between the number of rabbits y ( t ) and the number of foxes x ( t ) at any time t is given by − C ln y + Dy = A ln x − Bx + E where A , B , C , D , and E are constants. This relationship is based on a model by Lotka (1880-1949) and Volterra (1860-1940) for analyzing the ecological balance between two species of animals, one of which is a prey and the other a predator. Use implicit differentiation to find the relationship between the rate of change of the rabbit population in terms of the rate of change of the fox population.BuyFind*launch*

10th Edition

Soo T. Tan

Publisher: Brooks Cole

ISBN: 9781285464640

Chapter 5.5, Problem 87E

Textbook Problem

**Predator-Prey Model** The relationship between the number of rabbits *y*(*t*) and the number of foxes *x*(*t*) at any time *t* is given by

− *C* ln *y* + *Dy* = *A* ln *x* − *Bx* + *E*

where *A*, *B*, *C*, *D*, and *E* are constants. This relationship is based on a model by Lotka (1880-1949) and Volterra (1860-1940) for analyzing the ecological balance between two species of animals, one of which is a prey and the other a predator. Use implicit differentiation to find the relationship between the rate of change of the rabbit population in terms of the rate of change of the fox population.

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

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Price of Perfume The monthly demand for a certain...Ch. 5.4 - Price Of West The monthly demand for a certain...Ch. 5.4 - Spread of an Epidemic During a flu epidemic, the...Ch. 5.4 - Sales of a Product The total number of units of a...Ch. 5.4 - Elasticity of Demand The quantity demanded each...Ch. 5.4 - Elasticity of Demand Suppose that the demand...Ch. 5.4 - Weights of Children The Ehrenberg equation W =...Ch. 5.4 - Population Distribution The number of people...Ch. 5.4 - Optimal Selling Time Refer to Exercise 49, page...Ch. 5.4 - Maximum Oil Production It has been estimated that...Ch. 5.4 - Blood Alcohol Level Refer to Exercise 62, page...Ch. 5.4 - Price Of A Commodity The price of a certain...Ch. 5.4 - Thermometer Readiness A thermometer is moved from...Ch. 5.4 - Diffusion Suppose a cell of volume V is surrounded...Ch. 5.4 - Chemical Reaction Two chemicals, A and B, interact...Ch. 5.4 - Concentration Of A Drug In The Bloodstream The...Ch. 5.4 - Absorption Of Drugs A liquid carries a drug into...Ch. 5.4 - Absorption Of Drugs Refer to Exercise 85. 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In Exercises 51 and 52, use implicit...Ch. 5.5 - Find an equation of the tangent line to the graph...Ch. 5.5 - Find an equation of the tangent line to the graph...Ch. 5.5 - Determine the intervals where the function f(x) =...Ch. 5.5 - Determine the intervals where the function...Ch. 5.5 - Determine the intervals of concavity for the graph...Ch. 5.5 - Determine the intervals of concavity for the graph...Ch. 5.5 - Find the inflection points of the function f(x) =...Ch. 5.5 - Find the inflection points of the function f(x) =...Ch. 5.5 - Find an equation of the tangent line to the graph...Ch. 5.5 - Find an equation of the tangent line to the graph...Ch. 5.5 - Find the absolute extrema of the function f(x) = x...Ch. 5.5 - Find the absolute extrema of the function...Ch. 5.5 - In Exercises 65 and 66, find dy/dx by implicit...Ch. 5.5 - In Exercises 65 and 66, find dy/dx by implicit...Ch. 5.5 - In Exercises 67 and 68, find d2y/dx2 by implicit...Ch. 5.5 - In Exercises 67 and 68, find d2y/dx2 by implicit...Ch. 5.5 - Find dy/dx at the point (1, 1) using implicit...Ch. 5.5 - Find an equation of the tangent line to the graph...Ch. 5.5 - Strain On Vertebrae The strain (percentage of...Ch. 5.5 - Heights of Children For children between the ages...Ch. 5.5 - Average Life Span One reason for the increase in...Ch. 5.5 - Streaming Music Consumers are spending more on...Ch. 5.5 - Depreciation of Equipment For assets such as...Ch. 5.5 - Depreciation Of Equipment Refer to Exercise 75. A...Ch. 5.5 - Population Growth The population of a town t...Ch. 5.5 - Marginal Revenue The demand function for the...Ch. 5.5 - Maximizing Profit The manager of Seko, an...Ch. 5.5 - Lamberts Law Of Absorption Lamberts law of...Ch. 5.5 - Percentage Rate Of Growth Of A Company a. Show...Ch. 5.5 - Elasticity of demand a. In Section 3.4, we defined...Ch. 5.5 - Gompertz Function The Gompertz function defined by...Ch. 5.5 - Absorption of Light When light passes through a...Ch. 5.5 - Magnitude of Earthquakes On the Richter scale, the...Ch. 5.5 - Weber-Fechner Law The Weber-Fechner Law R=klnSS0...Ch. 5.5 - Predator-Prey Model The relationship between the...Ch. 5.5 - Rate of a Catalytic Chemical Reaction A catalyst...Ch. 5.5 - In Exercises 89 and 90, use the guidelines on page...Ch. 5.5 - In Exercises 89 and 90, use the guidelines on page...Ch. 5.5 - Derivative of bx a. Let f(x) = bx (b 0, b 1)....Ch. 5.5 - Derivative of logb x a. Let f(x) = logb x (b 0, b...Ch. 5.5 - In Exercises 93-96, use the results of Exercises...Ch. 5.5 - In Exercises 93-96, use the results of Exercises...Ch. 5.5 - In Exercises 93-96, use the results of Exercises...Ch. 5.5 - In Exercises 93-96, use the results of Exercises...Ch. 5.5 - In Exercises 97 and 98, determine whether the...Ch. 5.5 - In Exercises 97 and 98, determine whether the...Ch. 5.5 - Prove that ddxln|x|=1x(x0) for the case x 0.Ch. 5.5 - Use the definition of the derivative to show that...Ch. 5.6 - Give the model for unrestricted exponential growth...Ch. 5.6 - What is the half-life of a radioactive substance?Ch. 5.6 - What is the logistic growth function? What are its...Ch. 5.6 - Exponential Growth Given that a quantity Q(t) is...Ch. 5.6 - Exponential Decay Given that a quantity Q(t)...Ch. 5.6 - Growth Of Bacteria The growth rate of the...Ch. 5.6 - World Population The world population at the...Ch. 5.6 - World Population Refer to Exercise 4. a. If the...Ch. 5.6 - Resale Value Garland Mills purchased a certain...Ch. 5.6 - Atmospheric Pressure If the temperature is...Ch. 5.6 - Radioactive Decay The radioactive element polonium...Ch. 5.6 - Radioactive Decay Phosphorus 32 (P-32) has a...Ch. 5.6 - Nuclear Fallout Strontium 90 (Sr-90), a...Ch. 5.6 - Carbon-14 Dating Wood deposits recovered from an...Ch. 5.6 - Carbon-14 Dating The skeletal remains of the...Ch. 5.6 - Bank Failures In the wake of the 2008 financial...Ch. 5.6 - Online Shoppers The number of consumers...Ch. 5.6 - Exponential Growth Sales The sales of the Garland...Ch. 5.6 - Learning Curves The American Court Reporting...Ch. 5.6 - Drivers Licenses The percentage of teenagers and...Ch. 5.6 - Effect Of Advertising On Sales Metro Department...Ch. 5.6 - Demand For Computers Universal Instruments found...Ch. 5.6 - Reliability of Computer Chips The percentage of a...Ch. 5.6 - Lengths Of Fish The length (in centimeters) of a...Ch. 5.6 - Spread of an Epidemic During a flu epidemic, the...Ch. 5.6 - Growth of a Fruit Fly Population On the basis of...Ch. 5.6 - Demographics The number of citizens aged 45-64...Ch. 5.6 - U.S. Crude Oil Production The rate of production...Ch. 5.6 - Population Growth in the Twenty-First Century The...Ch. 5.6 - Dissemination of Information Three hundred...Ch. 5.6 - Price of a Commodity The unit price of a certain...Ch. 5.6 - Chemical Mixtures Two chemicals react to form a...Ch. 5.6 - Von Bertalanffy Growth Function The length (in...Ch. 5.6 - Absorption of Drugs The concentration of a drug in...Ch. 5.6 - Concentration of Glucose in the Bloodstream A...Ch. 5.6 - Radioactive Decay A radioactive substance decays...Ch. 5.6 - Logistic Growth Function Consider the logistic...Ch. 5.6 - a. Use the results of Exercise 34 to show that the...Ch. 5.6 - Logistic Growth Function Consider the logistic...Ch. 5.6 - Logistic Growth Function The carrying capacity of...Ch. 5.6 - Gompertz Growth Curve Consider the function Q(t) =...Ch. 5.6 - Air Travel Air travel has been rising dramatically...Ch. 5.6 - Newtons Law Of Cooling The temperature of a cup of...Ch. 5.6 - Computer Game Sales The total number of Stan...Ch. 5.6 - Population Growth in the Twenty-First Century The...Ch. 5.6 - Time Rate of Growth of a Timor The rate at which a...Ch. 5.6 - Annuities At the time of retirement, Christine...Ch. 5.6 - Absorption of Drugs The concentration of a drug in...Ch. 5.6 - Modeling with Data The snowfall accumulation at...Ch. 5 - The function f(x) = xb (b, a real number) is...Ch. 5 - a. The domain of the function y = 3x is _____, and...Ch. 5 - a. If b 0 and b 1, then the logarithmic function...Ch. 5 - a. If x 0, then eln x = ______. b. If x is any...Ch. 5 - In the compound interest formula A=P(1+rm)mt, A...Ch. 5 - The effective rate reff is related to the nominal...Ch. 5 - If interest earned at the rate of r per year is...Ch. 5 - a. If g(x) = ef(x), where f is a differentiable...Ch. 5 - a. In the unrestricted exponential growth model Q...Ch. 5 - a. For the model Q(t) = C Aekt describing a...Ch. 5 - Sketch the graphs of the exponential functions...Ch. 5 - In Exercises 2 and 3, express each equation in...Ch. 5 - In Exercises 2 and 3, express each equation in...Ch. 5 - In Exercises 4 and 5, solve each equation for x....Ch. 5 - In Exercises 4 and 5, solve each equation for x....Ch. 5 - In Exercises 6-8, given that ln 2 = x, ln 3 = y,...Ch. 5 - In Exercises 6-8, given that ln 2 = x, ln 3 = y,...Ch. 5 - In Exercises 6-8, given that ln 2 = x, ln 3 = y,...Ch. 5 - Sketch the graph of the function y = log2(x + 3).Ch. 5 - Sketch the graph of the function y = log3(x + 1).Ch. 5 - A sum of 10,000 is deposited in a bank. Find the...Ch. 5 - Find the interest rate needed for an investment of...Ch. 5 - How long will it take for an investment of 10,000...Ch. 5 - Find the nominal interest rate that yields an...Ch. 5 - In Exercises 15-32, find the derivative of the...Ch. 5 - In Exercises 15-32, find the derivative of the...Ch. 5 - In Exercises 15-32, find the derivative of the...Ch. 5 - In Exercises 15-32, find the derivative of the...Ch. 5 - In Exercises 15-32, find the derivative of the...Ch. 5 - In Exercises 15-32, find the derivative of the...Ch. 5 - In Exercises 15-32, find the derivative of the...Ch. 5 - In Exercises 15-32, find the derivative of the...Ch. 5 - In Exercises 15-32, find the derivative of the...Ch. 5 - In Exercises 15-32, find the derivative of the...Ch. 5 - In Exercises 15-32, find the derivative of the...Ch. 5 - find the derivative of the function. 26. f(x)=xlnxCh. 5 - find the derivative of the function. 27....Ch. 5 - find the derivative of the function. 28. y = (x +...Ch. 5 - find the derivative of the function. 29. y =...Ch. 5 - find the derivative of the function. 30....Ch. 5 - find the derivative of the function. 31....Ch. 5 - In Exercises 15-32, find the derivative of the...Ch. 5 - Find the second derivative of the function y = ln...Ch. 5 - Find the second derivative of the function y = x...Ch. 5 - Find h'(0) if h(x) = g(f(x)), g(x)=x+1x, and f(x)...Ch. 5 - Find h'(1) if h(x) = g(f(x)), g(x)=x+1x1, and f(x)...Ch. 5 - Use logarithmic differentiation to find the...Ch. 5 - Use logarithmic differentiation to find the...Ch. 5 - Find an equation of the tangent line to the graph...Ch. 5 - Find an equation of the tangent line to the graph...Ch. 5 - Sketch the graph of the function f(x) = xe2xCh. 5 - Sketch the graph of the function f(x) = x2 ln x.Ch. 5 - Find the absolute extrema of the function f(x) =...Ch. 5 - Find the absolute extrema of the function...Ch. 5 - INVESTMENT RETURN A hotel was purchased by a...Ch. 5 - Find the present value of 30,000 due in 5 years at...Ch. 5 - Find the present value of 119,346 due in 4 years...Ch. 5 - CONSUMER price Index At an annual inflation rate...Ch. 5 - GROWTH OF Bacteria A culture of bacteria that...Ch. 5 - RADIOACTIVE Decay The radioactive element radium...Ch. 5 - Demand for DVD Players VCA Television found that...Ch. 5 - Radioactivity The mass of a radioactive isotope at...Ch. 5 - Energy Consumption of Appliances The average...Ch. 5 - Oil Used to FUEL PRODUCTIVITY A study Oil...Ch. 5 - Price of a Commodity The price of a certain...Ch. 5 - FLU EPIDEMIC During a flu epidemic, the number of...Ch. 5 - World Population The world population is projected...Ch. 5 - U.S. INFANT MORTALITY rate The U.S. infant...Ch. 5 - Maximizing Revenue The unit selling price p (in...Ch. 5 - ABSORPTION OF DRUGS The concentration of a drug in...Ch. 5 - Solve the equation 1001+2e0.3t = 40 for t.Ch. 5 - Find the accumulated amount after 4 years if 3000...Ch. 5 - Find the slope of the tangent line to the graph of...Ch. 5 - Find the rate at which y = x ln (x2 + 1) is...Ch. 5 - Find the second derivative of y = e2x ln 3x.Ch. 5 - The temperature of a cup of coffee at time t (in...

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