How do logistic and exponential growth differ?

Question

Isaiah Allen · Accepted Answer

Logistic is limited growth, and exponential is unbounded growth.

If the number of people, y, who have heard a rumor is growing at a rate proportional to how many have heard it, then we get the differential equation y' = ky, where y' = dy/dt. In this case the growth is exponential, and the solution is y = A #e^(kt)#. The graph keeps getting higher and steeper forever.

Christopher Allers · Answer

undefined Logistic growth and exponential growth differ in terms of the factors that influence their growth patterns and the eventual outcomes.

Exponential growth:
- Exponential growth occurs when a population increases at a constant rate over time.
- In exponential growth, the population size doubles at regular intervals.
- This growth pattern does not account for limiting factors such as resource availability or competition.
- Exponential growth leads to an accelerating growth curve that continues indefinitely in ideal conditions.

Logistic growth:
- Logistic growth occurs when a population's growth rate slows down as it approaches its carrying capacity, which is the maximum population size that an environment can support.
- Initially, logistic growth resembles exponential growth, but as the population nears its carrying capacity, the growth rate decreases.
- Logistic growth incorporates limiting factors such as resource availability, predation, and competition, which influence the population's growth rate.
- The growth curve of logistic growth is characterized by an initial rapid increase followed by a leveling off as the population reaches its carrying capacity.