Set 17: Exponential Functions (Intermediate)

Choice A is correct. Choice A is the correct answer. Solve for the cooling constant $k$. 1. Given: $T(5) = 150$, so $150= 70 + 110 e^{-5 k}$. 2. Isolate: $80= 110 e^{-5 k}$. 3. Divide: $e^{-5 k} = \frac{80}{110} = \frac{8}{11} \approx 0.727$. 4. Natural log: $-5 k = \ln(0.727) \approx -0.318$. 5. Solve: $k = \frac{0.318}{5} \approx 0.064 \approx 0.063$. Strategic Tip: Use given data points to find unknown constants in exponential models. Choice B is incorrect because this cooling rate is too fast. Choice C is incorrect because this is slightly too slow. Choice D is incorrect because this rate is way too fast.