Set 8: Exponential Functions (Advanced)

Choice A is correct. Choice A is the correct answer. Solve for $T$ when $R(T) = 5$. 1. Equation: $5= 50 e^{-0.1 T}$. 2. Divide: $0.1= e^{-0.1 T}$. 3. Natural log: $\ln(0.1) = -0.1 T$. 4. Solve: $T = \frac{\ln(0.1)}{-0.1} = \frac{-2.303}{-0.1} \approx 23.03 \approx 23$ K. Strategic Tip: $\ln(0.1) = -\ln(10) \approx -2.303$. Choice B is incorrect because this is too high. Choice C is incorrect because this is too low. Choice D is incorrect because this is way too high.