​Which of the following correctly represents the relationship between the rate of population growth and population size?​

Correct option is B

Explanation-

The logistic growth equation is:

$$\frac{dN}{dt} = rN \left(1 - \frac{N}{K} \right)$$

Where:
                          $$\frac{dN}{dt}$$​    = population growth rate
                           = population size
                           = intrinsic rate of increase
                          = carrying capacity of the environment

Growth rate is highest at $$N = \frac{K}{2}.$$​​
.
Growth is slow when N is very low (due to few individuals).

Growth slows down again as   approaches  (due to resource limitation).
Growth becomes zero at :      =

So, the correct answer is option b 
          
Incorrect options-

Option a: Upside-down version of the correct curve; doesn't match the equation.
Option c: Linear growth, does not show the slowdown near K; inaccurate.
Option d: Shows decline after K, but in logistic growth, the rate just becomes zero, not negative (unless overpopulation with mortality is modeled, which is beyond standard logistic growth).