Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Medical
  • 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

View full answer

NEET 2024 Most scoring concepts

    Just Study 32% of the NEET syllabus and Score up to 100% marks

Similar Questions

Trending Articles/News

anam-khan

Maharashtra NEET PG counselling 2024 round 1 registration deadline today; application fee
anam-khan

Mere existence of 40% disability does not bar student from pursuing MBBS course: Supreme Court
anam-khan

Bihar NEET UG Counselling 2024: Round 3 registration begins today; fee, important dates

Latest Question