Solving the logistic growth model

  • Thread starter Thread starter jwang34
  • Start date Start date
  • Tags Tags
    Growth Model
Click For Summary

Homework Help Overview

The discussion revolves around the logistic growth model represented by the differential equation dx/dt=rx(1-x/K), where r and K are constants. Participants are exploring methods to solve this equation, expressing uncertainty about their approaches and the integration process involved.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts separation of variables but expresses uncertainty about its application and whether an integration factor is needed. Other participants confirm that separation of variables is appropriate and suggest using partial fractions for integration. There are questions about the correct setup for integration and the handling of variables.

Discussion Status

Participants are actively discussing the steps involved in solving the logistic growth model. Some guidance has been provided regarding the use of separation of variables and partial fractions, but there is no explicit consensus on the complete method yet. The conversation indicates a productive exploration of the problem.

Contextual Notes

The original poster mentions feeling rusty and uncertain about their approach, which may indicate a lack of confidence in their understanding of the topic. There is also a reference to a specific expected outcome, which may influence the participants' discussions.

jwang34
Messages
11
Reaction score
0
The logistic growth model is the following:

dx/dt=rx(1-x/K), with r and K and as constants, and x is a function of t.

I'm really not sure where to begin. First I tried separation of variables, but that didn't work out (and I don't even know if I was doing it right). Should I even be looking for an integration factor in solving this? It looks simple...but I guess I'm rusty in this.

The end result is supposed to be:

x(t)=K/(1+ce^-rt) c=[K-x(0)]/x(0)

Second, I tried deriving this equation and getting it to look like the previous equation, but I think I'm missing somethings.

So just a tip or hint that can push me down the right track would be great. Thanks a lot!
 
Physics news on Phys.org
Separation of variables is the right way to go. It gives you an x integral you can do easily by partial fractions. The rest is algebra. Get started and if you get stuck let us know.
 
So separation of variables in this case would be A(t)dt+B(x)dx=0. So I would have dx/rx=(1-x/K)dt. Then, I should integrate both sides? Is this the right track?
 
Put ALL of the x's on one side with the dx.
 
So I get dx/(rx(1-(x/K))=dt. Then I should use partial fractions to integrate?
 
Exactly. Use partial fractions.
 

Similar threads

High School Deriving an asymmetric logistic growth model
  • · Replies 3 ·
Replies
3
Views
3K
Experimenting whether the diameter of a pot affects boiling time for water
  • · Replies 15 ·
Replies
15
Views
3K
Undergrad Solve Int. Eq.: Exponential Growth Diff. Eq.
  • · Replies 7 ·
Replies
7
Views
4K
Graduate Mathematical Connection between Cosmic Expansion and Exponential Growth
  • · Replies 24 ·
Replies
24
Views
3K
Two spring-coupled masses in an electric field (one of the masses is charged)
  • · Replies 1 ·
Replies
1
Views
1K
Ice cube in water: entropy calculation (Calorimetry)
  • · Replies 6 ·
Replies
6
Views
1K
Initial velocity of bird landing on horizontal wire modeled as spring
  • · Replies 7 ·
Replies
7
Views
1K
Using Matlab ode45 to solve a simple 2 body problem
  • · Replies 5 ·
Replies
5
Views
5K
Understanding a math step in solving Schrödinger's equation for single particle in a box
  • · Replies 8 ·
Replies
8
Views
1K
How to solve a differential equation for a mass-spring oscillator?
  • · Replies 2 ·
Replies
2
Views
2K