please help A population of Monarch butterflies shows a tren

please help!

A population of Monarch butterflies shows a trend that suggests a logistic growth. If the carrying capacity is 500 butterflies and r = 0.1 individuals/(individuals x month), what is the maximum population growth rate for the population? (Hint: maximum population growth rate occurs when N = K/2).

Solution

please help!

A population of Monarch butterflies shows a trend that suggests a logistic growth. If the carrying capacity is 500 butterflies and r = 0.1 individuals/(individuals x month), what is the maximum population growth rate for the population? (Hint: maximum population growth rate occurs when N = K/2).

your answer :

as per question :

K = 500     

and r = 0.1

and the maximum population growth occured at N = (K/2)

SO THE MAXIMUM POPULATION SIZE WILL BE > K/2 = 500/2 = 250

WE KNOW THE logistic growth equation IS

dN/dt = rN[1-N/K]

SO,

dN/dt = (0.1)(250) [1 - (250)/500)]

Or,

dN/dt = 12.5 individuals/month

so the maximum population growth rate for the population is 12.5 individuals/ month ( answer)