​Populations of two species (A and B) follow logistic growth. The parameter values for the logistic growth equation are given in the table below.​

​Select the option that correctly gives the population growth rate at N = 100 for both species.​

Correct option is B

EXPLANATION-

To solve this question on logistic population growth, we will use the logistic growth formula:

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

Where:
r = intrinsic growth rate
N = current population size
K = carrying capacity
$$\frac{dN}{dt}$$​= population growth rate

Step 1: Calculate growth rate for Species A:

$$\frac{dN_A}{dt} = 2.5 \times 100 \times \left(1 - \frac{100}{500}\right)$$$$= 2.5 \times 100 \times (1 - 0.2) = 2.5 \times 100 \times 0.8 = 200$$

​​​Step 2: Calculate growth rate for Species B:

​$$\frac{dN_B}{dt} = 0.8 \times 100 \times \left(1 - \frac{100}{1000}\right)$$$$= 0.8 \times 100 \times (1 - 0.1) = 0.8 \times 100 \times 0.9 = 72$$

so, the correct option is (b) - Species A = 200 , Species B = 72

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