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notsponge [240]
2 years ago
3

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.
Biology
2 answers:
alukav5142 [94]2 years ago
8 0

Answer:

5 butterflies/month

Explanation:

Given -

Carrying capacity of the population of glasswing butterflies

= K = 200\\

The maximum per capita growth rate of the population of butterflies

= r = 0.10

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

= \frac{K}{2} \\= \frac{200}{2} \\= 100

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

\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 butterflies/month

Masteriza [31]2 years ago
7 0
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. 

Thank you for your question. Please don't hesitate to ask in Brainly your queries. 
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