The formula $N_t = N_0 e^{rt}$ represents which type of growth?

$A$ force which acts against the achievement of the highest possible level of population growth is known as:

Give scientific reasons: When a plant culture is grown in a limited amount of nutrient medium,growth is slow in the initial stage (lag phase). It increases rapidly in the exponential phase and again slows down in the stationary phase.

Given below are two statements.
Statement $I$: Under unlimited resource conditions,every species is capable of growing exponentially.
Statement $II$: $A$ population growing in a habitat with limited resources initially shows a very slow rate of growth.
In the light of the above statements,choose the correct option.

Ecological factors which prevent a species from producing at its maximum rate is termed as

In a forest, there are initially $100$ deer. Over a certain period, $30$ are born and $10$ die. Assuming food is abundant and predators are few, calculate the intrinsic rate of natural increase for that population.