Question

Suppose you are growing lettuce in plastic trays. You found out that your lettuce culture follows a logistic growth model with r=0.1 g/g.day and K=100 g per tray.

What is the maximal number of grams of lettuce could you harvest per day to keep your lettuce cultures at a constant size?

Answer 1

`(dN)/(dt)=2.5 g/day`

Explanation:

The logistic model equation is a differential equation, given by:

`(dN)/(dt)=r\left((K-N)/(K) \right)N`

Now, in this particularly model the optimum yield is at K/2. This value is the population here, so N=K/2.

`(dN)/(dt)=0.1\left((100-(100/2))/(100) \right)(100/2)`

`(dN)/(dt)=2.5 g/day`

Have a nice day!