Set 17: Exponential Functions

Choice A is correct. Choice A is the correct answer. Solve for $t$ using continuous compounding. 1. Formula: $30000= 15000 e^{0.065 t}$. 2. Divide: $2= e^{0.065 t}$. 3. Natural log: $\ln(2) = 0.065 t$. 4. Solve: $t = \frac{\ln(2)}{0.065} = \frac{0.693}{0.065} \approx 10.66 \approx 10.7$ years. Strategic Tip: Doubling time for continuous growth: $t = \frac{\ln(2)}{r}$. Choice B is incorrect because this is too long. Choice C is incorrect because this is too short. Choice D is incorrect because this doesn't match the calculation.