**Population Growth and Logistic Models****Scenario:**Suppose a population grows according to a logistic model with an initial population of 200 and a carrying capacity of 2,000. If the population grows to 500 after one year, what will the population be after another three years?**Explanation:**In this scenario, we are using a logistic growth model to predict population changes over time. Logistic growth considers the carrying capacity, which is the maximum population size that the environment can sustain. - **Initial Population:** 200- **Carrying Capacity:** 2,000- **Population after 1 Year:** 500The task is to determine the population size after an additional three years. Logistic growth is characterized by an initial period of rapid growth when the population is far below the carrying capacity, followed by a slowdown as the population approaches the carrying capacity.To solve this problem, one would typically use the logistic growth equation and solve for the time variable, continuing the calculation based on given parameters.

The logistic differential equation is dPdt=kP1-PL, where L is the carrying capacity. The solution of…

Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, what will the population be after another three years?

Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, what will the population be after another three years?

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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: 1. Suppose a population of rabbits starts with 30 rabbits. 60 days later, the population is 120…

Q: Suppose we are modelling the spread of the zombie virus throughout our class, and notice that it…

A: 1. a . The number of instructors initially are 10 . C0=10. The doubling time given is , t=3.5 days.…

Q: Is the logistic equation separable?

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: In a printing shop, print requests arrive randomly and independently at an average rate of 20 per…

A: i).Given:Time taken for 1 request=1.25Thus, time taken for 5 request=1.25*5=6.25 The formula and…

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

A: Given- Assume there is a certain population of fish in a pond whose growth is described by the…

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

A: If the starting population is given by P0 equals 200, then we have to find after one breeding season…

Q: Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the…

A: Population growth is studied using the exponential growth model.

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

Q: 2. Many countries have a population growth rate of 3% (or more) per year. At this rate, how many…

A: * SOLUTION :- (2)

Q: Use the logistic growth model to predict the population of a species after three years given the…

A: Solution:

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

Q: Suppose customers arrive to a single server at the rate of 1/2 customers per minute. The capacity of…

A: Let us solve the word problem in the next step.

Q: My home uses two light bulbs. On average, a light bulb lasts for 100 days (exponentially…

A: Possible states are 0, 1, and 2. Birth = a bulb is repaired while Death = bulb burns out. Then the…

Q: Define log-linear models?

A: To define log-linear models.

Q: Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the…

Q: the logistic equation.

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

Q: The yearly Chinese growth rate for population is increasing at about .35% per year. Construct an…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

**Population Growth and Logistic Models**

**Scenario:**
Suppose a population grows according to a logistic model with an initial population of 200 and a carrying capacity of 2,000. If the population grows to 500 after one year, what will the population be after another three years?

**Explanation:**
In this scenario, we are using a logistic growth model to predict population changes over time. Logistic growth considers the carrying capacity, which is the maximum population size that the environment can sustain.

- **Initial Population:** 200
- **Carrying Capacity:** 2,000
- **Population after 1 Year:** 500

The task is to determine the population size after an additional three years. Logistic growth is characterized by an initial period of rapid growth when the population is far below the carrying capacity, followed by a slowdown as the population approaches the carrying capacity.

To solve this problem, one would typically use the logistic growth equation and solve for the time variable, continuing the calculation based on given parameters.

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

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

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?
The population in a city is increasing in accordance with exponential growthmodel. The population on year 2016 was 1000 and the population on year 2021 is 2000. What will be the population in year 2026?
Suppose a variable is growing continuously at a nominal rate of 10% per year. What is the effective growth rate?
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 =
4. Suppose that sodium pentobarbitol is used to anesthetize a dog. The dog anesthetized when its bloodstream contains at least 40 mg of sodium pentobarbitol per kg of the dog's weight. Suppose that the sodium pentobarbitol is eliminated exponentially from the dog's bloodstream with a half-life of 6 hours. What single dose should be administered in order to anesthetize a 55- kg dog for 2.25 hours?
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 1200 fish. Absent constraints, the population would grow by 110% 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 =