Answer:
The solution is
.
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