Question

Assuming P≥0, suppose that a population develops according to the logistic equation
dP/dt=0.03P−0.00015P^2
where tt is measured in weeks. Answer the following questions.
1. What is the carrying capacity?

I tried solving the differential equation and got 600 but it says it's wrong what am I doing wrong??
Carrying Capacity:
1
2. What is the value of kk?
Answer: k=k=
1

3. For what values of PP is the population increasing?
Answer (in interval notation):

4. For what values of PP is the population decreasing?
Answer (in interval notation):

Answer 1

dp/dt=0.03p−0.00015p^2
This is a Bernoulli equation, with solution

200 e^<sup><sup>0.03t</sub></sub> / (e^<sup><sup>c</sub></sub>+e^<sup><sup>0.03t</sub></sub>)

No idea what k is supposed to be, or the carrying capacity. You will need some more info to determine c.

Since dp/dt = 0.00015p(200-p)
its roots are at p=0 and p=200

So, p is growing until it reaches 200, then starts decreasing. The problem is, p never reaches 200. So, p is always increasing. Read up on logistic growth.