Set 12: Exponential Functions

Choice A is correct. Choice A is the correct answer. Solve for $t$ when $C(t) = 100$. 1. Equation: $100= 500 e^{-0.15 t}$. 2. Divide: $0.2= e^{-0.15 t}$. 3. Natural log: $\ln(0.2) = -0.15 t$. 4. Solve: $t = \frac{\ln(0.2)}{-0.15} = \frac{-1.609}{-0.15} \approx 10.73 \approx 10.7$ minutes. Strategic Tip: For decay to reach 1/5 of original: $\ln(0.2) \approx -1.609$. Choice B is incorrect because this is slightly too long. Choice C is incorrect because this is too short. Choice D is incorrect because this is way too long.