Question 4. A herd consisting of 100 antelopes is introduced in a game farm. Theirpopulation growth is approximated by a logistic equation of the formdPP= rP(1dt6000with an intrinsic growth rate of Inper year. Suppose the solution of the differentialequation can be written in the formP,KP(t) =Po+ (K- P)e-rtwhere K is the carrying capacity of the logistic equation and Po is the initial value of thedifferential equation:a) Predict the population of the herd of antelopes after 15 years.b) At what time is the population growing the fastest?

Given that, A herd consisting of 100 antelopes is introduced in a game farm. Their population growth…

Answered: Question 4. A herd consisting of 100…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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JHU reports Covid-19 statistics daily for each US state as a function of time t, in days. These include P(t) - Cumulative Conﬁrmed Cases: total number of cases conﬁrmed before day t. In each case below, write the differential equation (the change equation) for P P for that state. That is write P'= . . . a. Covid cases in New York increase by 500 a day. P'= _________ b. West Virginia's Covid cases grew by 1.75% a day. P'=__________ The US population, U, in millions, has a 1.1% birth rate and a 0.8% death rate. About 1 million people immigrate into the US a year, and 0.08 million people emigrate from the US each year. Write the differential equation (the change equation) for U. That is write U'=. . . 2. a.) Now, 2021, there are 330 million people in the US. Using your differential equation, estimate the change in the number of millions of people in the US in the next year. Give two digits after the decimal point. Do not write millions in the answer box---just the…
For a Pacific halibut population, the value of r is 0.71 per year, and the environmental carrying capacity is 89 thousand tons of fish.† (a) Find the time it takes the population to grow from the optimum yield level to 87% of carrying capacity if the number b in the logistic growth equation is 1.5. (Round your answer to three decimal places.) yr(b) Find the time it takes the population to grow from the optimum yield level to 87% of carrying capacity if the number b in the logistic growth equation is 4.8. (Round your answer to three decimal places.) yr
Consider a time-varying population that follows the logistic population model. The population has a limiting population of 800, and at time t = 0, its population of 200 is growing at a rate of 60 per year. Please write a differential equation for the populatoin P(t) that models this scenario.
Exercise 0.2.12: Is there a solution to y' = y, such that y(0) = y(1)? Exercise 0.2.13: The population of city X was 100 thousand 20 years ago, and the population of city X was 120 thousand 10 years ago. Assuming constant growth, you can use the exponential population model (like for the bacteria). What do you estimate the population is now?
Please don't provide handwritten solution ....
1. A population grows continuously at the rate of 8% per year. How long does it take for the population to double ? Use differential equation it.
A bacteria population has logistic growht pattern with initial population 1000 and equilibrium population of 10.000. A count shows that at the end of 1 hour there are 2000 bacteria present. a)Write the initial value problem for the phenomena and determine the population as a function of time. b)Determine the time time at which the population is increasing more rapidly.
Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1000 fish. Absent constraints, the population would grow by 190% per year.If the starting population is given by �0=300, then after one breeding season the population of the pond is given by�1 = After two breeding seasons the population of the pond is given by�2 =
Assuming a carrying capacity for world population K = 15 billion, and a population of 7.75 billion as of 2020, estimate the year when population will reach 12 billion, assuming a logistic growth curve applies and with a current growth rate ro = 1.1% per year. What will the updated growth rate rf be in that future year when population reaches 12 billion?
Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 2000 fish. Absent constraints, the population would grow by 190% per year.If the starting population is given by �0=500, then after one breeding season the population of the pond is given by�1 = After two breeding seasons the population of the pond is given by�2 =
23. A population grows according to the logistic growth model, with growth parameter r = 0.8. Starting with an initial population given by po = 0.3, a) Find p₁ (report your answer to 4 decimal places) = 0.168 b) Find p2 (report your answer to 4 decimal places) = 0.1128 X c) Determine what percent of the habitat's carrying capacity is taken up by the 3rd generation. (Report your answer to 2 decimal places) 0.08 X %
During the period from 1790 to 1930, a country's population P(t) (t in years) grew from 3.7 million to 118.6 million. Throughout this period, P(t) remained close to the solution of the initial value dP problem = 0.03145P-0.0001486P², P(0) = 3.7. dt (a) What 1930 population does this logistic equation predict? (b) What limiting population does it predict? (c) The country's population in 2000 was 350 million. Has this logistic equation continued since 1930 to accurately model the country's population?

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