Posted by **Mel** on Friday, May 25, 2012 at 9:03am.

Someone please help! Have spent ages stressing over this and still can't figure out how to do it! need asap.

Question 3. In ecology, the logistic equation is often written in the form

dN divided by dt = rN(1-N/K)

where N = N(t) stands for the size of the population at time t, the constants r

and K stand for the intrinsic growth rate and the carrying capacity of the species,

respectively.

A pond on a sh farm has carrying capacity of 1000 sh, intrinsic growth rate

0.3 (when time is measured in months) and is originally stocked with 120 sh.

(a) Set up a logistic equation for the sh population N(t) in the pond, with t

measured in months.

(b) Find the size of the population when t = 10.

(c) Can the population reach 1000 at any future time?

even just recommendations on how to begin would be appreciated!

thanks :)

- Math -
**MathMate**, Friday, May 25, 2012 at 9:33am
dN/dt = rN(1-N/K)

is a separable equation by rewriting it as:

dN/[rN(1-N/K)] = dt

=>

(K/r)[1/(N(K-N))]dN = dt

split into partial fractions

(1/r)[1/N + 1/(K-N)]dN = dt

Now integrate

(1/r)(ln(N)+ln(K-N))=t + C

Rewriting,

ln(N*(K-N))=r(t+C)

At this point, substitute r and K to find constant C at time t=0.

Hint: C is between 38 and 39.

After that, use the equation to solve for required unknowns.

- Math -
**Mel**, Friday, May 25, 2012 at 9:42am
thank you so much!

- Math :) -
**MathMate**, Friday, May 25, 2012 at 9:52am
You're welcome!

## Answer this Question

## Related Questions

- chemistry - This question I really don't get it. I tried tried tried to figure ...
- Algebra - I am having such a hard time in this class. Hopefully someone here can...
- 5th Grade Math - I need help on how to figure out compund area of a shape. I ...
- chemistry -repost - Still can't figure this one out-- sorry for reposting, this...
- Math (Ms. Sue! Someone help) - Hi I really need help. I don't know even how to ...
- Chemistry - Determine the unknown quantity in the following cell at 298.15 K. Pt...
- math - If P0 > c (which implies that −1 < a < 0), then the ...
- ALGEBRA 1 - solve by graphing 3x+2y=8 6x+4y=16 You need to graph the 2 equations...
- Algebra - I've been trying to figure out this equation for over an hour but all ...
- Algebra - I know that standard form is Ax+By=C, but I'm not really sure how to ...

More Related Questions