Set 12: Exponential Functions (Intermediate)

Choice A is correct. Choice A is the correct answer. Compare growth rates over time. 1. Investment A: $A_A(t) = 5000(1.06)^t$. 2. Investment B: $A_B(t) = 7000(1.04)^t$. 3. Long-term: Higher growth rate (6% vs 4%) dominates. 4. Crossover: Eventually, $5000(1.06)^t > 7000(1.04)^t$ as $t$ increases. 5. Test $t=20$: - A: $5000(1.06)^{20} \approx 16,036$ - B: $7000(1.04)^{20} \approx 15,346$ Strategic Tip: In exponential functions, the base (growth rate) dominates in the long run. Choice B is incorrect because despite higher initial value, lower rate loses. Choice C is incorrect because different rates mean different growth. Choice D is incorrect because we can compare by calculating.