Concept:
Population growth depends on availability of resources such as food, space and nutrients.
Step 1: Understand unlimited growth condition.
When resources are not limiting, population increases rapidly.
\[
\text{Unlimited resources} \Rightarrow \text{rapid population growth}
\]
Step 2: Identify the growth curve.
Under unlimited resource conditions, population follows exponential growth.
\[
N_t=N_0e^{rt}
\]
where,
\[
N_t=\text{population at time }t
\]
\[
N_0=\text{initial population}
\]
\[
r=\text{growth rate}
\]
Step 3: Compare with logistic growth.
Logistic growth occurs when resources become limiting and carrying capacity is reached.
\[
\therefore \text{Correct Answer is (A)}
\]