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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?

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whitneytr12

Answer:

[tex]\frac{dN}{dt}=2.5 g/day[/tex]

Step-by-step explanation:

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

[tex]\frac{dN}{dt}=r\left(\frac{K-N}{K} \right)N[/tex]

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

[tex]\frac{dN}{dt}=0.1\left(\frac{100-(100/2)}{100} \right)(100/2)[/tex]

[tex]\frac{dN}{dt}=2.5 g/day[/tex]

Have a nice day!

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