Exponential growth refers to the increase in the growth of the population with respect to the time. Carrying capacity of the ecosystem refers to the number of living individuals in the population an ecosystem can sustain in terms of availability of resources like food, shelter, water, mates and other.
The healthy population will likely to decrease after experiencing exponential growth because the carrying capacity of a region will not be able to sustain the growth of increase in number of individuals. Therefore, the population will start to decline under the condition of insufficient carrying capacity.