Set 13: Exponential Functions (Advanced)

Choice A is correct. Choice A is the correct answer. Solve for $t$ when $H(t) = 1000$. 1. Equation: $1000= 100 e^{0.12 t}$. 2. Divide: $10= e^{0.12 t}$. 3. Natural log: $\ln(10) = 0.12 t$. 4. Solve: $t = \frac{\ln(10)}{0.12} = \frac{2.303}{0.12} \approx 19.19 \approx 19.2$ months. Strategic Tip: Memorize $\ln(10) \approx 2.303$ for quick calculations. Choice B is incorrect because this is too long. Choice C is incorrect because this is too short. Choice D is incorrect because this is way too long.