# Thread: Need Help in Logistic Model of Population

1. ## Need Help in Logistic Model of Population

I need help in how to create logistic model of population. I have data in ten years. The model is P(t)=K/(1+L^{-Mt}) where P(t) is population in time t. K,L,M is parameters. I dont know how to find K,L,M in that problem. Please help me.

2. ## Re: Need Help in Logistic Model of Population

Substitute three of your data points into the equation, this will give you three equations in three unknowns to solve simultaneously

3. ## Re: Need Help in Logistic Model of Population

Thank you so much. Now I get 3 complicated equation? Please give me some suggestion how to solve it..

4. ## Re: Need Help in Logistic Model of Population

Show me what you have so far...

5. ## Re: Need Help in Logistic Model of Population

I make it into 2 equation:
first : 120.7 + (675.5*L)/e^{3M} - (554.8*L)/e^M = 0
second : 66.5 + (675.5 *L)/e^{3M} - (609*L)/e^{2M}=0

and I dont know what to do again

6. ## Re: Need Help in Logistic Model of Population

I dont know how to use latex here, could you tell me?

7. ## Re: Need Help in Logistic Model of Population

How did you get these two equations?

8. ## Re: Need Help in Logistic Model of Population

I substitute three of my data points into the equation, and I substitute one into two remains equation, and I get those two..

9. ## Re: Need Help in Logistic Model of Population

I mean, I substitute three of my data points into the equation. From those three, I pick one and I substitute this into two remains equation, and I get those two..

10. ## Re: Need Help in Logistic Model of Population

Originally Posted by AyuAbstractAlgebra
I mean, I substitute three of my data points into the equation. From those three, I pick one and I substitute this into two remains equation, and I get those two..
Tell me the three equations you started with please, because your method doesn't sound right.

11. ## Re: Need Help in Logistic Model of Population

Here are they:
$\displaystyle K=554.8(1+\frac{L}{e^M})$
$\displaystyle K=609(1+\frac{L}{e^{2M}})$
$\displaystyle K=675.5(1+\frac{L}{e^{3M}})$

And then, I substitute the 3rd to 1st and 2nd equation

12. ## Re: Need Help in Logistic Model of Population

Here are they:
$\displaystyle K=554.8(1+\frac{L}{e^M})$
$\displaystyle K=609(1+\frac{L}{e^{2M}})$
$\displaystyle K=675.5(1+\frac{L}{e^{3M}})$

And then, I substitute the 3rd to 1st and 2nd equation

13. ## Re: Need Help in Logistic Model of Population

Why only use three of the points?