Answered: 1-How are the birth rate and death rate…

1-How are the birth rate and death rate defined for a population model? You may answer this by discussing the units of the birth rate and death rate.

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: Suppose a population grows according to a logistic differential equation model. Its population in…

A: It is given that the population in years 2000 and 2001 is 500 and 1500 respectively and carrying…

Q: The median value of a home in a particular market is decreasing exponentially. If the value of a…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: The amount of fish in a lake is modeled by the logistic equation: = 2y(4 – y). If a certain amount…

A: Given, Logistic model of the fish in the lake is y'=2y(4-y). rate of catching fish is h, then…

Q: a) A maintenance staff member of the company has found that water tank is affected by some bacteria…

Q: At a suburban high school, information spreads by word of mouth according to the logistic function…

A: We are given an logistic function Here k is the growth rate and t is the time. Observe from the…

Q: (a) Assume that the carrying capacity for the US population is 800 million. Use it and the fact that…

Q: dy 2. When does the differential equation Cekt represent exponential growth? exponential dt decay?

A: We need to explain growth and decay.

Q: 4) The student population at a certain school here in Dagupan can be modeled by the logistic growth…

A: You must have idea about growth model to understand it better.

Q: 3. Log-linearize the equation, x, +a = (1-b)

Q: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had…

Q: The natural resources of an island limit the growth of the population to a limiting value of 4,526.…

Q: Studies to fit a logistic model to the Eastern Pacific yellowfin tuna population have yielded 148 N=…

Q: 7. A commercial fishery is estimated to have carrying capacity 40 tons of salmon. Suppose the annual…

Q: 65. Population growth. Before 1859, rabbits did not exist in Australia. That year, a settler…

A: (a) Determine the value for k from the given differential equation. P=8900,…

Q: Suppose a population is growing according to the logistic formula N = 470 1 + 3e-0.41t' where t is…

A: We have to find the value of N and t

Q: e. Discuss the solutions to the differential equation. What are the equilibrium points of the model?…

Q: Assume that the population of a city satisfies the logistic hypothesis: "The rate of change of…

A: Let the year 1960 is denoted by t=0.Therefore year 2000 is denoted by: t=40Let the population at…

Q: The population of ants in a colony grows at a rate proportional to the number of ants P present at…

A: Given that the ants grow at a rate proportional to its population P at time t. i.e. dPdt α P ⇒dPdt =…

Q: 5. A population of butterflies is released into a den and is growing according to the logistic…

A: Logistic equation: The differential equation that describes the logistic population model is given…

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…

Q: Consider two populations that can be modeled by the logistic equation with the same carrying…

A: We are given two population modeled by logistic equations having same carrying capacity but…

Q: For a Pacific halibut population, the value of r is 0.71 per year, and the environmental carrying…

A: a) We have to find time in logistic growth: Rate per year,r=0.71 Population growth,N=77,430 Value of…

Question

1-How are the birth rate and death rate defined for a population model? You may answer this by discussing the units of the birth rate and death rate.

2-For the equation dP/dt=KP(M−P), where K>0 and M>0, why is the constant M known as the carrying capacity?

3-For a population described by the logistic differential equation, what will happen if the initial population is above the carrying capacity?

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Remark

Step 2: Step 1

Step 3: Step 2

Solution

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

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?
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.
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
At time t = 0, a bacterial culture weighs 2 grams. Three hours later, the culture weighs 5 grams. The maximum weight of the culture is 20 grams. (a) Write a logistic equation that models the weight of the bacterial culture. (Round your coefficients to four decimal places.) 20 y = dy dt = 1 +9e 8 g (c) When will the culture's weight reach 16 grams? (Round your answer to two decimal places.) 9.79 hr (d) Write a logistic differential equation that models the growth rate of the culture's weight. Then repeat part (b) using Euler's Method with a step size of h = 1. (Round your answer to the nearest whole number.) y(5) = 6 -0.3662t = 1.37 0.366y| 1 (1-20) (b) Find the culture's weight after 5 hours. (Round your answer to the nearest whole number.) X g (e) At what time is the culture's weight increasing most rapidly? (Round your answer to two decimal places.) hr
7. A commercial fishery is estimated to have carrying capacity 40 tons of salmon. Suppose the annual growth rate of total salmon population P (measured in tons) is governed by the logistic equation P' = P(1 – P/40) and initially there are 30 tons of fish. (i) What is the fish population after 1 year? (You may use e 2 2.72.) Suppose that the owner of the fishery decides to harvest h tons of salmon annually at a constant rate. Then (ii) ( What is the differential equation governing the fish population now? (iii) What is the maximun sustainable harvesting rate? (Justification is required.)
Please please answer both a and b Thank you so much
In 30 min
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