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.

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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Assume there is a certain population of fish in a pond whose growth is described by the logistic…

A: The logistic equation describes the growth of a certain population of fish in a pond.The pond's…

Q: Suppose that the growth-rate parameter k = 0.3 and the carrying capacity N = 2500 in the logistic…

A: Given that, The growth-rate parameter k = 0.3. The carrying capacity N = 2500. Suppose P(0) = 2500.…

Q: (d) At what time will there be 16 grams of substance Br years (e) of which substance is there less…

A: B(t) = 16

Q: Suppose that we estimate a logit model based on an intercept and two explanatory variables A-0.1,…

Q: Suppose I am interested in modeling how wages are determined. My model of interest is log(wage) = β0…

A: Hey, since there are multiple sub-part questions posted, we will answer first three sub part…

Q: A population of bees in a particular region satisfies the logistic equation with carrying capacity…

Q: Assume there is a certain population of fish in a pond whose growth is described by the logistic…

A: The objective of this question is to calculate the population of fish in a pond after one and two…

Q: The logistic model can also be changed by incorporating a constant continuous rate of decrease, such…

A: Consider the given equation. dPdt=kP1-PA-H Put x=PA in the above equation. dxdt=1AdPdt Put all the…

Q: Consider the logistic growth model for population growth: dy/dt = 10-4y(1000-y)=0.10y(1-(y/1000))…

A: solution- you have posted a question with multiple subpart , we will solve first three for you . to…

Q: Some populations initially grow exponentially but eventually level off. Equations of the form P (t)…

A: Given,

Q: A population of 200 bass released in a lake began growing at a rate of 100 fish/yr. A second…

Q: If we are modeling a herd of clk, with an initial population of 100, in a region with a carrying…

A: Given that The population of elk satisfies a logistic growth model and Initial population = 100…

Q: The total number of reported cases of an illness in a large city tt days after the start of an…

A: Given the logistic differential equation is: y'=15600y1400-y…1 The standard form of a logistic…

Q: Populations that can be modeled by the modified logistic equation dP dt P(bP-a) can either trend…

Q: Assume a simple logistic regression model for X and Y. We know: bo= -1.1 and b₁ = 0.4 Estimate P(Y=…

Q: Suppose that a population grows according to a logistic model with carrying capacity 5700 and k =…

Q: The number N() of people In a community who are exposed to a particular advertisement is governed by…

Q: The Adams County Helath Department predicts that about 20% of the County's population, or about 7500…

A: We will substitute all values in the given function to get relation between a,b,c and then find…

Q: Biologists release two otters (a type of water animal) into a river. They believe that the river…

A: Detailed explanation:Part i: Finding α and βGiven:Carrying capacity K=500Intrinsic growth rate…

Question

Please write a differential equation for the populatoin P(t) that models this scenario.

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given

VIEW

Step 2: Intermediate step

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

Can you identify an appropriate solution technique and solve this differential equation, too? Thank you!

Solution

by Bartleby Expert

SEE SOLUTION

Similar questions

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 two populations that can be modeled by the logistic equation with the same carrying capacity, but with different values of k. Which population approaches the carrying capacity most quickly, the one with the smaller or larger value of k? You may want to think geometrically (check out some slope fields), analytically (look at the form of the solution), or num into the solution). erically (plug some t values
Suppose the probability π(x)π(x) of reaching a target (such as getting a ball between goal posts) as a function of distance x (in metres) from the target is well-fitted by a logistic regression equation withlog(π(x)/[1−π(x)])=6.1−0.13xPlease answer below to 3 significant digits.Part a)For this prediction model, what is the probability of reaching the target from a distance of 49 metres.Part b)At what distance is the probability of reaching the target equal to 0.6?
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?
Suppose the population of a species of animals on an island is governed by the logistic model with relative rate of growth k = 0.05 and carrying capacity M= 15000. I.e., the population function P(t) satisfies the equation P' = bP(15000 - P), where b = k/M. If the current population is P(0) = 20000, which one of the following is closest to P(1)? O a) 19700 O b) 19890 Oc) 19680 Od) 19690 Oe) 19805 Of) 19742 Motion
please show clear, thanks
We estimate the following model for wages for major league baseball players: ln⁡(salary)= β0 +β1years + β2gamesyr + β3frstbase + β4scndbase + β5shrtstop + β6thrdbase + β7outfield + u where ln(salary) = the natural log of a player’s salary years = the player’s years in the major league gamesyr = the player’s average number of games played per year and frstbase, scndbase, shrtstop, thrdbase and outfield are each a dummy variable equal to 1 if the player plays that position on the field (when their team is fielding) and 0 otherwise. These are mutually exclusive dummy variables and there is one omitted fielding position, catcher. We find: *Regress lsalary years gamesyr frstbase scndbase shrtstop thrdbase outfield Source SS df MS Model Residual 300.454626 191.720909 7 345 42.9220894 0.55571278 Total 492.175535 352 1.39822595 lsalary coef. std. err. t P > |t| [95% Conf. Interval] years 0.0672574 0.0125509 5.36 0.000…
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 =
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 =
During the period from 1790 to 1920, a country's population P(t) (t in years) grew from 3.6 million to 101.6 million. Throughout this period, P(t) remained close to the solution of the initial value problem -0.0001494P² P(0) = 3.6. dP dt = 0.03136P-( (a) What 1920 population does this logistic equation predict? (b) What limiting population does it predict? (c) The country's population in 2000 was 259 million. Has this logistic equation continued since 1920 to accurately model the country's population? (a) The logistic equation predicts the population in 1920 to be million. (Do not round until the final answer. Then round to the nearest thousandth as needed.) K AI C H TU U →> C ¢ ➡ H i O + 2.4 e В → نه Y + - 8 .... : *** 5 Ø Co Less . N 0 .. H A E X U i 9 A C ש Σ VI 8 FR > in X