Set 8: Exponential Functions

Choice A is correct. Choice A is the correct answer. Identify the limiting value. 1. Logistic form: $P(t) = \frac{K}{1 + Ae^{-rt}}$ where $K$ is carrying capacity. 2. As $t \to \infty$: $e^{-0.5 t} \to 0$, so $P(t) \to \frac{1000}{1 + 0} = 1000$. 3. Carrying capacity: The maximum population is 1,000. Strategic Tip: In logistic growth, the numerator is always the carrying capacity. Choice B is incorrect because 9 is the coefficient $A$, not the limit. Choice C is incorrect because this is the initial population $P(0) = \frac{1000}{10} = 100$. Choice D is incorrect because this is half the carrying capacity.