Set 15: Exponential Functions

Choice A is correct. Choice A is the correct answer. Compare growth factors over the long term. 1. Investment P: $P(t) = 1000(1.10)^t$. 2. Investment Q: $Q(t) = 800(1.15)^t$. 3. Long-term: $1.15> 1.10$, so Q's base is larger. 4. Conclusion: As $t \to \infty$, the larger base dominates, so Q eventually exceeds P. Strategic Tip: In exponential growth, larger base always wins in the long run. Choice B is incorrect because despite higher initial value, lower growth rate loses. Choice C is incorrect because different bases mean they diverge. Choice D is incorrect because we can determine this from the growth rates.