Gompertz Function The model is a differential equation that is solved using the

Question

Gompertz Function
The model is a differential equation that is solved using the separation of variables technique.
The Gompertz Function Equation is given by
dP/dt=k ln(M/P)P
Where k is a constant, P is the population at any time t, and M is the carrying capacity
of the environment (the maximum population the environment can support).

Consider a population of beavers in wetlands where the carrying capacity of the
environment is 60 beavers. Scientists initially counted 8 beavers. After three years,
they counted 15 beavers.

1. Solve the specific Gompertz differential equation for this beaver population.
2. Use the population equation you derived to evaluate P ( 6) , P ( 10) and
P ( 100) and interpret your results.
3. Compute lim-(t?8)??P(t)? and explain your result.
4. Graph the P ( t ) function.
5. Show from the differential equation that the Gompertz function grows fastest
when P=M/e







I just need help on getting started. If anyone has done this exact equation or one similar any help would be appriciated.

Explanation / Answer

hint : dP / { p [ ln m - ln P ] } = k dt.......let w = ln M - ln P for an easy integration

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.