Set 12: Exponential Functions

Choice A is correct. Choice A is the correct answer. Evaluate the logistic function at $t=0$. 1. Substitute: $P(0) = \frac{5000}{1 + 49 e^0} = \frac{5000}{1 + 49}$. 2. Simplify: $P(0) = \frac{5000}{50} = 100$. 3. Result: Initial population is 100. Strategic Tip: For logistic $P(t) = \frac{K}{1 + Ae^{-rt}}$, initial value is $\frac{K}{1+A}$. Choice B is incorrect because this is the carrying capacity, not initial population. Choice C is incorrect because this is $1 +A$ (the denominator at $t=0$). Choice D is incorrect because this is half the carrying capacity.