Math
posted by Mel .
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(1N/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 :)

dN/dt = rN(1N/K)
is a separable equation by rewriting it as:
dN/[rN(1N/K)] = dt
=>
(K/r)[1/(N(KN))]dN = dt
split into partial fractions
(1/r)[1/N + 1/(KN)]dN = dt
Now integrate
(1/r)(ln(N)+ln(KN))=t + C
Rewriting,
ln(N*(KN))=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. 
thank you so much!

You're welcome!
Respond to this Question
Similar Questions

Algebra
I know that standard form is Ax+By=C, but I'm not really sure how to do this problem. All help is welcome. Thanks in advance. Write an equation for each line: through (1,3) and parallel to y=2x+1 I know that the slop will be 2 because … 
Algebra
I am having such a hard time in this class. Hopefully someone here can help me to understand some of what they are trying to teach me. I have a problem here and have been working on it for about an hour now and I can not figure it … 
5th Grade Math
I need help on how to figure out compund area of a shape. I meen we have the math part of the CRCT tommorow and I'm STILL NOT sure how to do it? 
chemistry
This question I really don't get it. I tried tried tried to figure out how to start solve the problem but still couldn't figure out. So can you help me with one question PLEASE? 
chemistry repost
Still can't figure this one out sorry for reposting, this is the last post, if someone has time to review this question and see if they can figure out how the textbook got 1.0x10^7 seconds Iodine combines to form I2 in liquid propane … 
Math (Ms. Sue! Someone help)
Hi I really need help. I don't know even how to figure these two questions out so if you could help me, please. Is (–4, 10) a solution to the equation 10 – 5x = y? 
Differential equation
A first order linear equation in the form y′+p(x)y=f(x) can be solved by finding an integrating factor μ(x)=exp(∫p(x)dx) (1) Given the equation (x+4)^2y′+5(x+4)y=16 find μ(x)= I found it to be e^(5ln(x+4))which … 
Math(Quadratic Functions)
Determine the quadratic function, f(x), with x intercepts at x=7 and x=2 and y intercept at y=5. I have been struggling with this question for days. I have phoned my teacher and gotten her help, but I still can't figure it out. If … 
Math
I have 2 questions that I need help with if someone could please help me step by step to figure out how to do this equation it would be very helpful. Thank you 1. Suppose y varies directly with x and, y=15 and x=5. Write a direct variation … 
math
i need help on my unit 4 lesson seven 24 question unit tst from connexus academy.i am a level nine gymnast and have a huge meet that im stressing out about and so i cant focus someone please help me thank you