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Sergio039 [100]
3 years ago
12

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?
Mathematics
1 answer:
Charra [1.4K]3 years ago
5 0

Answer:

\frac{dN}{dt}=2.5 g/day

Step-by-step explanation:

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

\frac{dN}{dt}=r\left(\frac{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.

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

\frac{dN}{dt}=2.5 g/day

Have a nice day!

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