5. Another equation that has been used to model population growth is the Gompertz equation dP...

5. Another equation that has been used to model population growth is the Gompertz equation dP /dt = rP ln (K P ) , where r and K are positive constants, and P(t) > 0.

(a) Sketch a clearly labeled graph of f(P), where dP/dt = f(P) (state the main facts you used to obtain your answer).

(b) Draw the phaseline. Next to it, sketch a set of integral curves in the t − P plane.

(d) (Extra Credit) For 0 < P < K, find P 00(t) and determine where the graph of P(t) is concave up and where it is concave down. Enter the inflection point in your graph in (a). (Enter your answer in an attached blank page.)

Solutions

Expert Solution

Feel free to ask doubts in the commemt section and give it a thumbs up if you liked the answer. Have a good day.

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Another model for a growth function for a limited population is given by the Gompertz function,...

Another model for a growth function for a limited population is given by the Gompertz function, which is a solution to the differential equation dP/dt=cln(K/P)P where c is a constant and K is the carrying capacity. Answer the following questions 1. Solve the differential equation with a constant c=0.15, carrying capacity K=3000, and initial population P0=1000 Answer: P(t)=? 2. With c=0.15, K=3000, and Po=1000, find limt→∞P(t). Limit:?

Consider the Solow growth model with population growth and growth in the efficiency of labor. Suppose...

Consider the Solow growth model with population growth and growth in the efficiency of labor. Suppose that 2 countries A and B have the same production function given by Yt = Ktα(LtEt)1−α, the same rate of growth of E (g), the same depreciation rate of physical capital (δ) and the same saving rate s. The initial level of E, E0, is lower in country A than in country B. (a) Compare the steady-state levels of output per effective worker of...

The dire prediction of economic growth based upon the Classical growth model has not been very...

The dire prediction of economic growth based upon the Classical growth model has not been very accurate. What is this prediction and why hasn't it they come true?

A population of fish in a lake follow a logistic growth model. With an initial growth...

A population of fish in a lake follow a logistic growth model. With an initial growth rate of 10%, an initial population of 50, and a carrying capacity of 500, how many fish will be in the pond after 5 years? Solve and graph the solution to this equation. Explain why this differential equation does or does not serve as a realistic model.

Another of the assumptions of the basic SIR model is that the population does not lose...

Another of the assumptions of the basic SIR model is that the population does not lose the immunity once it has been acquired. But in real life that doesn't always happen. In the basic model, make the necessary modifications to include the case in which the population loses immunity and is again susceptible to illness. Perform a full model analysis.

Global warming has been linked to the growth of population of some insects and pests in...

Global warming has been linked to the growth of population of some insects and pests in cooler areas where they have not been previously seen. What global systems does this population growth affect? Identify a positive and a negative feedback resulting from it.

The Shumpeterian Growth Model (5 marks) What is the “Creative Destruction” in the Shumpeterian Growth Model?...

The Shumpeterian Growth Model What is the “Creative Destruction” in the Shumpeterian Growth Model? What are the positive and negative effects of a higher success rate of innovation on the relative size of a 1 research sector?

Population Exponential Model: Suppose that the growth rate of the population of city X is proportional...

Population Exponential Model: Suppose that the growth rate of the population of city X is proportional to the population of X. We have the following data: the population in 1945 was 36,000 and the population in 1990 was 63,000. Establish and solve an Initial Value Problem to express the population of X as a function of time, graph this function and calculate an estimate of the population in the year 2040. Solve the problem using the parameters from the beggining...

Contrast the H-D model with the Solow model, and explain the impact of population growth on...

Contrast the H-D model with the Solow model, and explain the impact of population growth on income per head and economic development. Relate your answer to a particular country of your own choosing.

Select a good that you previously used, but has been replaced by another good. (For example,...

Select a good that you previously used, but has been replaced by another good. (For example, Apple iPods replacing Sony Walkmans.) Analyze the transition from one good to another, and the effects on prices. (For example, what did the rise of the iPod do to the price of Walkmans.)

Subjects