A logistic growth curve includes limits (like resource scarcity and crowding), so it rises at first but then slows and levels off at a carrying capacity, forming an S‑shaped (sigmoid) curve, whereas an exponential growth curve assumes no limits, so it keeps speeding up and forms a J‑shaped curve. Logistic growth is therefore more realistic for long‑term populations in real environments, while exponential growth is a short‑term idealization under unlimited resources.

Core idea

  • Exponential growth:
    • Population grows at a constant per‑capita rate with effectively unlimited resources.
    • Produces a J‑shaped curve that becomes steeper over time.
  • Logistic growth:
    • Starts similarly to exponential growth but slows as resources run short and competition increases.
    • Produces an S‑shaped curve that levels off at the carrying capacity, the maximum population the environment can sustain.

Visual shapes

  • Exponential curve:
    • Low at first, then sharply shoots upward with no upper bound (J‑shape).
  • Logistic curve:
    • Initially shallow, then rapidly increases, and finally bends and flattens as it approaches a horizontal upper limit (S‑shape).

Limits and carrying capacity

  • Exponential model:
    • Ignores limits such as food, space, and disease; no built‑in maximum population size.
  • Logistic model:
    • Explicitly includes limiting factors; growth slows as population nears carrying capacity and stabilizes around that value.

When each applies

  • Exponential growth fits:
    • Short‑term growth of populations introduced into a new, resource‑rich environment (e.g., bacteria in a fresh nutrient medium).
  • Logistic growth fits:
    • Longer‑term population dynamics where resources are finite, such as animals in a bounded habitat.

In many real systems, what looks exponential early on often turns out to be logistic once limits start to bite and the curve bends toward a plateau.

Quick TL;DR:
Exponential = unlimited, ever‑steepening J‑curve. Logistic = starts exponential, then slows and levels into an S‑curve because of carrying capacity and limits.

Information gathered from public forums or data available on the internet and portrayed here.