Choice A is the correct answer. Evaluate the logistic function at $t=0$.

1. Substitute: $P(0) = \frac{5000}{1 + 49e^0} = \frac{5000}{1 + 49}$.
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.