Suppose the population of the world was about 6.2 billion in 2000. Birth rates around that time ranged from 35 to 40 million per year and death rates ranged from 15 to 20 million per year. Let'sassume that the carrying capacity for world population is 20 billion.(a) Write the logistic differential equation for these data. (Because the initial population is small compared to the carrying capacity, you can take k to be an estimate of the initial relative growthrate. Calculate k using the maximum birth rate and maximum death rate. Let t = 0 correspond to the year 2000.)dPdt=(b) Use the logistic model to estimate the world population (in billions) in the year 2010. (Round your answer to the nearest hundredth.)billionCompare this result with the actual population of 6.9 billion.This result ---Select---the actual population of 6.9 billion.EACHER(c) Use the logistic model to predict the world population (in billions) in the years 2100 and 2500. (Round your answers to the nearest hundredth.)billionbillion21002500

The population of the world was about 6.2 billion in 2000. Birth rates that time ranged from 35 to…

Answered: Suppose the population of the world was…

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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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 120% per year. If the starting population is given by po = 500, then after one breeding season the population of the pond is given by P1 = Round your answer to the nearest integer.
In the early 1980s, AIDS (Acquired Immune Deficiency Syndrome) spread rapidly. A logistic curve modeling the spread of the disease in the United States is given by 47500 P(t) = 1+ 148.41e-0.8t where t is measured in years since 1981 and P is the number of reported cases. In what year does this model predict that the number of new cases will be growing at the largest rate? Remember to fully justify your answer.
Consider the following estimated model, where the dependent variable is the log of the hourly wage: log(wage) = 0.417 +0.17educ +0.0295tenure - 0.00059tenure? educ = level of education, in years tenure = duration of tenure, in years What is turnaround value (or turning point) for tenure?
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
Show that for a population that satisfies the logistic model, the maximum rate of growth of population size is rK/4, attained when population size is K/2.
1. World Wildlife fund (WFO) releases 25 Leopar... Start your trialnow! First week only $4.99! Want to se 1. World Wildlife fund (WFO) releases 25 Leopards into a game preserve in Kyrgyzstan. After 2 years, there are 39 leopards in the preserve. The WFO game preserve park in Kyrgyzstan has a carrying capacity of 200 panthers. a. Write a logistic equation that models the population of leopard in the preserve. b. Find the population after 5 years. When will the population reach 100? d. Write a logistic differential equation that models the growth rate of the leopard population. At what time is the leopard population growing most rapidly? Explain. C. e. Cookies and Personal Information This site uses cookies to improve performance, personalize your experience, analyze usage and assist our marketing efforts, but we don't sell your personal data as defined in the CA Consumer Privacy Act. To opt of the use of third-party targeting cookies, check "Do Not Sell My Personal Information" and then…
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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 1600 fish. Absent constraints, the population would grow by 230% per year.
Assume that the population of a town can be modeled by the logistic equation dP/dt = kP(1000 - P). If this town's population was 800 five years ago and is 850 this year, what is its population expected to be five years from now? Round your answer to the nearest integer.
If a village has a population of 2000 and a natural growth rate of 3.7% but has a carrying capacity of 6000, what will the population be in 2 years time under the logistic growth model?
4.) (For Marketing & Sales Analysts-Consultants). Four months after the deliveries of goods were affected by the granular lockdown due to the Covid-19 pandemic, a manufacturer noticed that sales had dropped from 100,000 units per month to 80,000 units. If the sales follow an exponential pattern decline, what will they be after another 4 months? Note: Use the exponential model, y= Cekt, where t is measured in months.
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