The spread of a rumor in a group of people can be modeled by a logistic growth equation. In abusiness of 1000 employees, if 10% of the employees have heard the rumor at time t = 0 days andthe number of people who have heard the rumor is growing at a rate of 120 employees/day at thattime (hint: useful for finding r), find a differential equation to model this situation and solve it tofind a formula for the number of employees who have heard the rumor at time t. Sketch the phasegraph for your equation and clearly identify any equilibrium points and classify them by type.

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Answered: The spread of a rumor in a group of…

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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A biodiversity organization releases 1200 tilapia into a lake. After a year, there are 2000 tilapia in the lake. Assume that the growth of the population of tilapia follows the logistic model, and that the lake has a carrying capacity of 20400 for this species of tilapia. (a) Write a formula that gives the number of tilapia after t years. (b) When will the population reach 10000? (c) How fast is the population changing when there are 10000 tilapia in the lake?
The logistic growth function P(x) = 1+271e models the percentage, P(x), of Americans who are x years old and have some coronary heart disease. Use this function to find the age at which the percentage of Americans who have some coronary heart disease is 10%. What is the age at which 10% of Americans have some coronary heart disease? years old (Round to the nearest integer)
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.
Use the logistic growth model to predict the population of a species after three years given the specified growth rate and Po rate=4.4%; P = 0.55 At the end of three years, the population of a particular species is% of its maximum population. (Round to the nearest tenth as needed.)
In 2013, the moose population in a park was measured to be 5,600. By 2017, the population was measured again to be 9,700. If the population continues to change exponentially, find an equation for the moose population, P, as a function of t, the years since 2013. Round numbers to 3 decimal places as needed. What does your model from above predict the moose population to be in 2022?
The table below represents the number of clients for a company from 2018 to 2022 (t − 0 represents 2018): Year, t Clients(Thousands) 1 6 2 10 3 25 4 34 (a) Find a logarithmic regression model, f(t) = A ln t + C to represent the data. (b) Using the model, predict the number of users in 2023? (c) Using the model, when will the company exceed 5227 clients?
If the population of a Nigeria doubles in 9 years, ﬁnd the growth rate k. Assume that the population increases exponentially.
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?
A professor surveyed students on their study habits, where "x" is the number of hours studying and "y" is the resulting test score. Using a logarithmic regression, predict the number of hours needed to score 95. (Graph and equation in picture provided)
Due to the rising temperatures in a bay ecosystem, the population mass of a certain species of jellyfish is growing exponentially. When first measured in 2010 (which we can call year t = 0), the bay contained about 600 tons of jellyfish. Now in 2021 (t = 11), the bay has 2,000 tons. If it continues to grow in this way, in what year will the jellyfish population mass reach 10,000 tons?

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