Another model for a growth function for a limited population is given by the Gompertz function, which is a solution to the differential equation $$\frac{dP}{dt} = c \ln\left(\frac{K}{P}\right) P$$ where $c$ is a constant and $K$ is the carrying capacity. Answer the following questions.

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1. Solve the differential equation with a constant $c = 0.05,$ carrying capacity $K = 2000,$ and initial population $P_0 = 750.$
Answer: $P(t) =$

2. With $c = 0.05,$ $K = 2000,$ and $P_0 = 750,$ find $\displaystyle \lim_{t \to \infty} P(t).$
Limit:

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