In which population growth models is the population growth dependent on the current population size?

Explore the exponential growth model: In an exponential growth model, the population grows at a rate proportional to its current size. This means the larger the population, the faster it grows. The formula for exponential growth is often expressed as \( P(t) = P_0 e^{rt} \), where \( P(t) \) is the population at time \( t \), \( P_0 \) is the initial population size, \( r \) is the growth rate, and \( e \) is the base of the natural logarithm.

Investigate the logistic growth model: The logistic growth model also depends on the current population size, but it includes a carrying capacity, which is the maximum population size that the environment can sustain. The growth rate decreases as the population approaches the carrying capacity. The logistic growth equation is \( P(t) = \frac{K}{1 + \frac{K - P_0}{P_0} e^{-rt}} \), where \( K \) is the carrying capacity.