A population of glasswing butterflies exhibits logistic growth. The carrying capacity of the population is 200 butterflies, and rmax, the maximum per capita growth rate, of the population is 0.10 butterflies/(butterflies •month). calculate the maximum population growth rate for the population if the maximum growth occurs when N= k/2. Give your answer to the nearest tenth.

130.78

According to sources, the most probable answer to this query is that the maximum population growth rate for the population of butterflies depends on the niche they are in.

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Arclight Arclight · Answer 2 · 2019-09-18T18:03:18+02:00

Answer:

[tex]5[/tex] butterflies/month

Explanation:

Given -

Carrying capacity of the population of glasswing butterflies

[tex]= K = 200\\[/tex]

The maximum per capita growth rate of the population of butterflies

[tex]= r = 0.10[/tex]

The maximum population size is equal to half of the carrying capacity of butterflies

[tex]= \frac{K}{2} \\= \frac{200}{2} \\= 100[/tex]

The maximum population growth rate for the population if the maximum growth occurs when N= k/2

[tex]\frac{dN}{dt} = rN[1-\frac{N}{K}]\\\frac{dN}{dt} = (0.1)(100)[1-\frac{100}{200}]\\\frac{dN}{dt} = (0.1)(100)(0.5)\\\frac{dN}{dt} = 5[/tex] butterflies/month