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

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Step-by-step explanation:

We have the Gompertz's differential equation

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Notice that this a separable equation. So,

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Now, integrating in both sides:

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Recall that

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Thus,

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and taking exponential:

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Taking another exponential

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

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

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Then,

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Hence, the solution is

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step-by-step explanation:

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step-by-step explanation: