Set 12: Exponential Functions

Choice A is correct. Choice A is the correct answer. Find when concentration halves. 1. Half: $C(t) = 100$ (half of 200). 2. Equation: $100= 200 e^{-0.2 t}$. 3. Divide: $0.5= e^{-0.2 t}$. 4. Natural log: $\ln(0.5) = -0.2 t$. 5. Solve: $t = \frac{\ln(0.5)}{-0.2} = \frac{-0.693}{-0.2} \approx 3.47 \approx 3.5$ hours. Strategic Tip: Half-life formula: $t_{1/2} = \frac{\ln(2)}{k}$ for decay $e^{-kt}$. 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.