Another model for a growth function for a limited population is given by the gompertz function, which is a solution to the differential equation dpdt=cln(kp)p where c is a constant and k is the carrying capacity. answer the following questions. 1. solve the differential equation with a constant c=0.05, carrying capacity k=3000, and initial population p0=1000.

The solution is

.

Step-by-step explanation:

We have the Gompertz's differential equation

.

Notice that this a separable equation. So,

.

Now, integrating in both sides:

.

Recall that

.

Thus,

,

and taking exponential:

.

Taking another exponential

.

Now, let us substitute the given values for c and K:

.

To find the value of the constant A'' we use the initial condition:

.

Then,

.

Hence, the solution is

i really dont know

step-by-step explanation: