How Does the Alligator Population Change Over Time in a Swamp?

[saintdick]

This has been posted before but i didn't understand the answer

Suppose the number x(t) (with t in months) of alligators in a swamp satisfies the differential equation

dp/dt = 0.0001x^2 - 0.01x

(a) If there are initially 25 alligators in the swamp, solve this differential equation to determine what happens to the alligator population in the long run.

(b) Repeat for an initial population of 150 alligators."

i am totally clueless about this one?

 

[chiro]

Hey saintdick and welcome to the forums.

From your question it seems that p is actually the same as x(t) [i.e. p = x(t)] from the context of your question.

So basically the model is the same as saying:

dp/dt = 0.0001p^2 - 0.01p.

Using this information, what do you think the next step is?

 

[saintdick]

Ho chiro,

I used separtion of variable to get: dx/x(x-100)=dt/10000

integrated both side, used PFD for left side:

1/100 ln(x-100)-1/100 ln(x)= 1/10000 *t +c

now what? how do i solve this for x?

 

[chiro]

Ho chiro,

I used separtion of variable to get: dx/x(x-100)=dt/10000

integrated both side, used PFD for left side:

1/100 ln(x-100)-1/100 ln(x)= 1/10000 *t +c

now what? how do i solve this for x?

Yes you need to solve for x by using algebra and properties of logs.

Your integration constant will depend on your initial value which is different for each sub-question.

It may help if you post your final answer if you want someone to check it or if you run into trouble.