Question

In: Advanced Math

Let a logistic curve be given by dP/dt = 0.02*P*(50-P) with the initial condition P(0)=5 This...

Let a logistic curve be given by

dP/dt = 0.02*P*(50-P)

with the initial condition

P(0)=5

This is an IVP (“initial value problem”) for the population P versus time t.

Report the following numbers in the given order (use two digits):

  1. The growth coefficient k=?
  2. The carrying capacity M=?
  3. The population level when the growth just starts to slow down (“the inflection point” population level) PIP=?
  4. The time when the population just starts to slow down tIP=?
  5. The population level when t=5: P(5)=?
  6. The long-term approximation for the population level limit P(t) as t-> infinity.

Solutions

Expert Solution

For the first two questions, the given equation is being compared with the standard equation giving the logistic curve for population growth, and the values of k and M are obtained.

For the third and fourth questions, the IVP is solved and the time t and the population P are calculated at the point of inflection of the logistic curve.

The final two questions have not been answered based on QA guidelines.

Colby Messinger answered 2 years ago
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