The logistic equation below is often used for modeling animal populations. dP kP(M-P) (1) The independent...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The logistic equation below is often used for modeling animal populations. dP kP(M-P) (1) The independent variable is t, and the units of t must be specified implicitly, such as months or years or some other duration. The population P (here, the number of animals) is the dependent variable. As such, the logistic equation is an autonomous differential equation, meaning that the independent variable t does not appear explicitly in the equation. If the birth rate in the animal population being modeled is o and the death rate is 80 and the birth rate slows in proportion to the size of the population (modeled by the additional term ), then the rate of change of the population with time is described by: P(o - BP-80) (2) This kind of modulation of the birth rate is common is environments with limited resources. If the units of 0, B1, and 60 are all (months), then we are implicitly specifying that the units of t are months. Letting k = B1 and M = Boo, then eq. (1) results from eq. (2). B1 Given an animal population believed to be characterized by the following logistic equation coefficients, Bo = 0.12 / month B = 0.0005/month S = 0.08/month and an initial population (at t = 0) of 50 animals (that is, P(0) = 50), 1. Separate the variables of eq. (1) and find the general solution (i.e., one that includes the constant C) of the differential equation. 2. Rename the integration constant Po (instead of C) and rewrite your solution, applying the initial condition (P(O)) specified above. 3. How many months from t = 0 are expected for the animal population to reach 60? Round your answer to the nearest tenth of a month. 4. In two years, what is the animal population expected to be? Round your answer to the nearest integer. (This is an example of modeling populations with a continuous dependent variable when the number of animals P can only be a non-negative integer.) The logistic equation below is often used for modeling animal populations. dP kP(M-P) (1) The independent variable is t, and the units of t must be specified implicitly, such as months or years or some other duration. The population P (here, the number of animals) is the dependent variable. As such, the logistic equation is an autonomous differential equation, meaning that the independent variable t does not appear explicitly in the equation. If the birth rate in the animal population being modeled is o and the death rate is 80 and the birth rate slows in proportion to the size of the population (modeled by the additional term ), then the rate of change of the population with time is described by: P(o - BP-80) (2) This kind of modulation of the birth rate is common is environments with limited resources. If the units of 0, B1, and 60 are all (months), then we are implicitly specifying that the units of t are months. Letting k = B1 and M = Boo, then eq. (1) results from eq. (2). B1 Given an animal population believed to be characterized by the following logistic equation coefficients, Bo = 0.12 / month B = 0.0005/month S = 0.08/month and an initial population (at t = 0) of 50 animals (that is, P(0) = 50), 1. Separate the variables of eq. (1) and find the general solution (i.e., one that includes the constant C) of the differential equation. 2. Rename the integration constant Po (instead of C) and rewrite your solution, applying the initial condition (P(O)) specified above. 3. How many months from t = 0 are expected for the animal population to reach 60? Round your answer to the nearest tenth of a month. 4. In two years, what is the animal population expected to be? Round your answer to the nearest integer. (This is an example of modeling populations with a continuous dependent variable when the number of animals P can only be a non-negative integer.)
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
importance of workalike balance for women as a leader in healthcare. 1. The purpose of the research; 2. Research question/s; 3. Findings and relevant data; 4. Any recommendations and; 5. The...
-
What did Frederick Taylor, the proponent of scientific management, advocate for to achieve efficiency in manufacturing?
-
Explain what is meant by the term "accrued expense," including how an accrued expense arises and where it is reported in the financial statements.
-
Target Corporation prepares its financial statements according to U.S. GAAP. Target's financial statements and disclosure notes for the year ended January 30, 2016, are available in Connect. This...
-
What are the main features of class mobility in the United States?
-
LIFO Choices Wilkens Company uses the LIFO method for inventory costing. In an effort to lower net income, company president Lenny Wilkens tells the plant accountant to take the unusual step of...
-
A series RL circuit is powered by an alternating voltage source oscillating with angular frequency 3.9 rad/s and peak-to-peak voltage 74.0 V. It is connected in series to a 2.5 ohm resistor and a 1.6...
-
If the minimum points of all the possible short-run average total cost curves become successively lower as quantity of output increases, then: there are economies of scale the firm should try to...
-
Two adult entertainment establishments feature live nude dancing ("strip clubs") in City. Because the clubs are competing for customers, they buy advertisements on large electronic billboards in the...
-
e) The Miles and Ezzell (1980) model suggests that the model at (d) above explains the relationship between the asset and equity beta. The Hamada (1972) model suggests a different formula for...
-
Consider the following data DescriptionCost Cost of Materials Used$40,000 Direct Labor costs$55,000 Factory Overhead$32,000 Work in Process, beg$28,000 Work in Process, end$18,000 Finished Goods,...
-
Give an example of a type of business which might utilize high leverage ( gearing ) fully explaining how this would benefit them from a financial management perspective.
-
While parachuting, a 71.0 kg person experiences a downward acceleration of 2.60 m/s. What is the downward force Fperson on the parachute from the person? Ignore the effects of air resistance.
-
Good headlines and leads can make or break a story. Describe five popular templates for headlines and the strategies behind them. What do they all have in common? How do journalists incorporate...
-
A new car sold for $31,000. If the vehicle loses 15% of its value each year, how much will it be worth after 10 years?
-
The root mean square (rms) value of a function, \(x(t)\), is defined as the square root of the average of the squared value of \(x(t)\) over a time period \(\tau\) :...
-
The amplitudes of displacement and acceleration of an unbalanced turbine rotor are found to be \(0.5 \mathrm{~mm}\) and \(0.5 \mathrm{~g}\), respectively. Find the rotational speed of the rotor using...
-
Find the Fourier series expansions of the functions shown in Figs. 1.58(ii) and (iii). Also, find their Fourier series expansions when the time axis is shifted down by a distance \(A\). (d) (e) x(t)...
Study smarter with the SolutionInn App