# Logistic Equation Calculus Question

• saralsaigh
In summary, the question asks for the carrying capacity and value of k in a population that develops according to the logistic equation dp/dt = 0.03p - 0.006p^2, where t is measured in weeks. The equation can be rearranged to get it in the form dp/dt = rp(1-p/K), where r is the Malthusian parameter and K is the carrying capacity. The mistake made in the attempt was factoring out p^2, which resulted in a term looking like 1/p instead of p inside the brackets. The correct form is dp/dt = 0.006p(5-p) = 0.03p(1-p/5). By solving

## Homework Statement

Suppose that a population develops according to the logistic equation
dp/dt = 0.03 p - 0.006 p^2
where t is measured in weeks.
-What is the carrying capacity and the value of k?

## Homework Equations

dp/dt = kP ( 1 - (p/K)) where K is the carrying capacity

## The Attempt at a Solution

Well i thought that in order to solve this i need to get the differenctial expression give in the question to resemble that of the logistic equation so i can get the values. so far my attempts have failed...so i don't know if THAT is wat i am actually supposed to do.
I rearranged the equation and i got:
dp/dt = P^2 ( (o.o3/P) - 0.oo6)
= 0.006 P^2 ( (5/P) - 1)
= -0.006 P^2 ( 1- (5/P))
that is the farthest I went so far i don't really know wat to do next or whether or not I am understanding this question correctly. Any help would be greatly appreciated You have the general form, but then you factored out a p^2. Now you are inventing another form...

To paraphrase "Only Euclid has seen beauty bare" ... but not here.

So, you want to get your equation in the form $$\frac{dp}{dt}=\frac{rp(K-p)}{K}=rp(1-\frac{p}{K})$$, where here r is the Malthusian parameter (your k) and K is the carrying capacity.

Your mistake was factoring out p2, since this gives us a term which looks like 1/p instead of p inside the brackets. You should do this: $$\frac{dp}{dt}=0.006p(5-p)=0.03p(1-\frac{p}{5})$$. Can you solve now?

Last edited:
cristo said:
So, you want to get your equation in the form $$\frac{dp}{dt}=\frac{rp(K-p)}{K}=rp(1-\frac{p}{K})$$, where here r is the Malthusian parameter (your k) and K is the carrying capacity.

Your mistake was factoring out p2, since this gives us a term which looks like 1/p instead of p inside the brackets. You should do this: $$\frac{dp}{dt}=0.006p(5-p)=0.03p(1-\frac{p}{5})$$. Can you solve now?

thanks for the help i got the right answer 