The growth rate will be at its highest when there is both a population that is large enough to reproduce at a high rate and that has enough resources to sustain this.
Work Step by Step
Smaller and larger populations have smaller growth for different reasons. A smaller population has ample resources but fewer members that can reproduce, and a larger population has many reproductive members but limited resources to support them. In the middle, both barriers are mitigated somewhat, causing a higher rate of growth.