Set 6: Exponential Functions (Intermediate)

Choice A is correct. Choice A is the correct answer. Solve for $t$ when $A(t) = 500$. 1. Equation: $500= 50 e^{0.3 t}$. 2. Divide: $10= e^{0.3 t}$. 3. Natural log: $\ln(10) = 0.3 t$. 4. Solve: $t = \frac{\ln(10)}{0.3} = \frac{2.303}{0.3} \approx 7.68 \approx 7.7$ hours. Strategic Tip: $\ln(10) \approx 2.303$ is useful to remember. 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.