<u>Answer</u>: As the growth rate increases, the population size increases more rapidly. The slope becomes steeper.
An increasing growth rate means that more and more of the offspring will survive. Thus, this leads to a cumulative effect in which with an increasing growth rate, the slope becomes steeper.
If in the beginning only 1 out of 10 offspring will survive (r=0.1), then the population will increase with only one individual. However, if r=0.5 then 5 new individuals will be added. These in turn will be able to reproduce themselves with even higher r, which results in the cumulative effect mentioned above. The more individuals survive and the higher r, the faster the population size will increase.
No ecosystem is capable of sustaining such a growth for long periods of time. The population will reach and exceed a level called carrying capacity, which is the maximum number of individuals the ecosystem can sustain. Once this happens, the growth rate will be negative until the population size is once more under this level.
From now on, the population will vary around the carrying capacity with r switching from positive to negative in a continuous cycle. Furthermore, if this level is exceeded very much, then currently available resources will be consumed and thus the population size will plummet back to extremely low levels.
Locust swarms are a good example. The population size increases rapidly and devours all available food. If no more food can be found, then the majority of the individuals will die of starvation.
