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  • A population grows according to the logistic growth equation, dN/dt=rN(1-N/K)  where dN/dt is the rate of population growth, r is the intrinsic rate of increase, N i

A population grows according to the logistic growth equation, dN/dt=rN(1-N/K)  where dN/dt is the rate of population growth, r is the intrinsic rate of increase, N is population size and K Is the carrying capacity of the environment.

According to this equation, population growth rate is maximum at

 

Option: 1

K/4


Option: 2

K/2


Option: 3

K


Option: 4

2K


Answers (1)

best_answer

According to the logistic growth equation, the population growth rate is given by \mathrm{\frac{dN}{dt}=rN(1-\frac{N}{K})}, where dN/dt represents the rate of population growth, r is the intrinsic rate of increase, N is the population size, and K is the carrying capacity of the environment.

To determine the point at which the population growth rate is maximum, we can find the value of N that maximises the expression \mathrm{rN(1 - \frac{N}{K})}.

To find the maximum, we can take the derivative of the expression with respect to N and set it equal to zero:

\mathrm{\frac{d}{dN}(rN(1-\frac{N}{K}))=r(1-2\frac{N}{K})=0}

Solving for N, we get :

\mathrm{1-2\frac{N}{K}=0}

        \mathrm{2\frac{N}{K}=1}

            \mathrm{2=\frac{K}{2}}

Therefore, the population growth rate is maximum at \mathrm{N=\frac{K}{2}}.

The correct answer is option 2 that is \mathrm{\frac{K}{2}}

Posted by

rishi.raj

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