# Thread: Need to solve an equation for a constant value.

1. ## Need to solve an equation for a constant value.

dL/dt = k(1-L)

This is a logistic function, if I'm not mistaken.

It's a lab in my DE book. I need to find my personal k value. It's about rate of memorization.

It says I can use numerical methods or analytic methods. The problem is I don't know how to do either, apparently. I have my data, I just don't know how to apply it.

Any help?

2. Originally Posted by pantsaregood
dL/dt = k(1-L)

This is a logistic function, if I'm not mistaken.

It's a lab in my DE book. I need to find my personal k value. It's about rate of memorization.

It says I can use numerical methods or analytic methods. The problem is I don't know how to do either, apparently. I have my data, I just don't know how to apply it.

Any help?
Can you not separate the variables?

$\frac{dL}{1-L} = k \, dt$

3. Yes.

It comes out to

L = e^kt + 1

I don't really see how this allows me to solve for k, since I have several L and t values. Those values all require k to be something different.

ln(L-1)/t = k

I have ten different values for L and t. How do I work with that?

4. Originally Posted by pantsaregood
Yes.

It comes out to

L = e^kt + 1

I don't really see how this allows me to solve for k, since I have several L and t values. Those values all require k to be something different.

ln(L-1)/t = k

I have ten different values for L and t. How do I work with that?
I have as solution of the DE [imath]L(t)=1-A\cdot e^{-k\cdot t}[/imath] Now you have two unknown parameters "A" and "k" which you can find by applying the least squares method on your data with this equation.

Coomast