Which of the following statements is correct?
a) The number of organisms can increase but never decrease once a population reaches its carrying capacity.
b) All population experience exponential growth once they reach carrying capacity.
c) A population always grows rapidly once it reaches its carrying capacity.
d) Limiting factors can influence the number of organisms in a population once it reaches its carrying capacity.

In the following equation of Verhulst - Pearl logistic growth, the letter $\text{'}\mathrm{r}\text{'}$ denotes ___ .

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

The shape of the pyramids reflects the growth status of the population. Identify the type of age pyramid represented below for human population.

Read the following data carefully

Imagine the lion population grows logistically where the carrying capacity is $800.$ Then the per capita birth rate$\left(\mathrm{b}\right)$, per capita death rate$\left(\mathrm{d}\right)$, intrinsic rate of natural increase$\left(\mathrm{r}\right)$, increase or decrease in population during the unit time period $\left(\frac{dN}{dt}\right)$ are respectively