- #1

clynne21

- 11

- 0

## Homework Statement

consider a lake that is stocked with walleye pike and that the pike population is governed by P'=.1P(1-P/10) where time is measured in days and P is thousands of fish. Suppose that fishing is started in this lake and that 100 fish are removed daily. modify the logistic model to account for the fishing

## Homework Equations

P'=.1P(1-P/10)

## The Attempt at a Solution

I am thinking it's just P'=.1P(1-P/10)-.1 but that seems too easy LOL. any thoughts?

## Homework Statement

Suppose a population is growing according to the logistic eqn

dP/dt=rP(1-P/K)

Prove that the rate at which the population is increasing is at its greatest when the population is at one-half of it's carrying capacity.

*Hint: Consider the second derivative of P*

## Homework Equations

dP/dt=rP(1-P/K)

## The Attempt at a Solution

Absolutely no idea where to start with this one :-(