Set 16: Exponential Functions (Advanced)

Choice A is correct. Choice A is the correct answer. Apply the continuous compound interest formula. 1. Formula: $A = Pe^{rt}$ where $P = 8000$, $r = 0.05$, $t = 10$. 2. Calculate exponent: $rt = 0.05 \times 10 = 0.5$. 3. Compute: $A = 8000 e^{0.5} = 8000(1.6487) \approx 13,181.23$. 4. Result: After 10 years, the investment is worth $13,181.23. Strategic Tip: Continuous compounding uses base $e$, which grows faster than annual compounding. Choice B is incorrect because this assumes simple interest (8000 + 4000). Choice C is incorrect because this calculation is wrong. Choice D is incorrect because this uses annual compounding, not continuous.