Calculus PLSSSSS HELP DUE SOON
posted by Regina on .
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):

dp/dt=0.03p−0.00015p^2
This is a Bernoulli equation, with solution
200 e^^{0.03t / (e^c+e^0.03t) 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(200p) 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.}