6
advanced-math

Which statement about exponential vs logistic growth is TRUE?

A

Logistic growth has a carrying capacity; exponential doesn't

B

Exponential growth eventually levels off

C

Logistic growth is always faster

D

Both have the same long-term behavior

Correct Answer: A

Choice A is the correct answer. Compare the two growth models.

  1. Exponential: y=abxy = ab^x grows without bound (no limit).
  2. Logistic: y=K1+Aerty = \frac{K}{1 + Ae^{-rt}} approaches carrying capacity KK.
  3. Key difference: Logistic has a maximum (realistic for populations), exponential doesn't.

💡 Strategic Tip: Exponential = unlimited growth. Logistic = limited by resources.

Choice B is incorrect because exponential growth never levels off. Choice C is incorrect because logistic starts slow, speeds up, then slows. Choice D is incorrect because their long-term behaviors differ completely.