What is the Carrying Capacity of a Stocked Lake?

[the7joker7]

Homework Statement

Biologists stocked a lake with `400` fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be `6900`. The number of fish doubled in the first year.

Homework Equations

The Attempt at a Solution

I know how to do everything in this problem once I find little k. Only issue is...I can't find little k.

I thought it would be the ln(2) = .693, but it's .757, and I can't figure out how that answer got there. Once I can find k, I can do the rest easily.

 

[MasterTinker]

Can I ask which equations you used? And what do they want you to find? Once you tell me that I can give a good rundown of methods on finding the constant...

 

[the7joker7]

I didn't really use any equations. I just thought I recalled from some classwork we did that, since the amount of fish doubled in one year, k would be the ln(2). I know there's a way to prove that, but I don't recall it at the moment. But that wasn't correct.

 

[MasterTinker]

hmmmm, okay, unfortunately the way I would do this is with differential equations... I can't really tell whether you're in high school or not, would using them be okay? If not I would just personally go to a homework helper, I would only see an equation and throw it at you unless its something that I've worked with recently...

 

[the7joker7]

No, I'm in college. This is a calculus class I'm in. IIRC, you don't actually NEED calculus to solve this problem, but if you want to use it that's fine.

 

[HallsofIvy]

If you are in college then you must have learned some common sense!

You wrote:

I know how to do everything in this problem once I find little k. Only issue is...I can't find little k.

and, when asked what equations you were talking about,

I didn't really use any equations. I just thought I recalled from some classwork we did that, since the amount of fish doubled in one year, k would be the ln(2).

Now, how is that going to make anys sense to us when you haven't told us what "k" means! If you could do the problem is that you "can't find little k", at least tell us what equation you would put "littel k" into!

 

[MasterTinker]

I guess that's the bets way to put it, although you can sometimes go off of classwork to really solve the problem you needto understand what's going on... have you solved it yet or can you show me a presentation of the original problem?