How can carrying capacity be related to population increase?
The inflection point of the logistic growth model is half the carrying capacity. So, population will act like the exponential function below half the carrying capacity.
When the population is above half the carrying capacity, growth will slow more quickly as you get closer to the carrying capacity.
However, if population is above the carrying capacity, population will decrease because there won't be enough resources to sustain the population.
If you are more specific with the question, you will get a more specific answer.