Set 11: Exponential Functions

Choice A is correct. Choice A is the correct answer. Use the shifted exponential model. 1. Model: $T(t) = (T_0 - T_{\text{room}})(b)^t + T_{\text{room}}$. 2. Given: $T_0 = 95$, $b = 0.9$, $T(10) = 59.38$. 3. Set up: $59.38= (95 - T_{\text{room}})(0.9)^{10} + T_{\text{room}}$. 4. Solve: $(0.9)^{10} \approx 0.3487$, so: $$59.38= (95 - T_{\text{room}})(0.3487) + T_{\text{room}}59.38= 33.13 - 0.3487 T_{\text{room}} + T_{\text{room}}26.25\approx 0.6513 T_{\text{room}}$T_{\text{room}} \approx 20°\text{C}$ Strategic Tip: The horizontal asymptote represents room temperature in cooling problems. Choice B is incorrect because room temperature isn't freezing. Choice C is incorrect because this doesn't match the calculation. Choice D is incorrect because this is too warm.