Set 8: Exponential Functions

Choice A is correct. Choice A is the correct answer. Solve for $t$ when $U(t) = 10000$. 1. Equation: $10000= 500 e^{0.15 t}$. 2. Divide: $20= e^{0.15 t}$. 3. Natural log: $\ln(20) = 0.15 t$. 4. Solve: $t = \frac{\ln(20)}{0.15} = \frac{2.996}{0.15} \approx 19.97 \approx 20$ months. Strategic Tip: Always isolate the exponential term before taking logarithm. Choice B is incorrect because this only gives about 4,480 users. Choice C is incorrect because this assumes growth rate of 0.015, not 0.15. Choice D is incorrect because this gives about 4,945 users.