1. **State the problem:** We want to find which function best models the temperature $T(m)$ of iced tea $m$ minutes after it starts warming, given initial and subsequent temperatures. 2. **Given data:** - Room temperature (ambient): 70°F - Initial temperature at $m=0$: 21°F - Temperature at $m=5$: 36°F - Temperature at $m=10$: 47°F 3. **Understanding the problem:** The iced tea warms towards room temperature, so the temperature approaches 70°F as $m$ increases. 4. **Check each function at $m=0$:** - (A) $T(0) = 21(1.71)^0 = 21$ (matches initial temperature) - (B) $T(0) = 21(0.58)^0 = 21$ (matches initial temperature) - (C) $T(0) = (70 - 21)(0.73)^{0/5} = 49 \times 1 = 49$ (does not match initial temperature) - (D) $T(0) = 70 - 49(0.69)^{0/5} = 70 - 49 \times 1 = 21$ (matches initial temperature) 5. **Evaluate functions at $m=5$ and compare to 36°F:** - (A) $T(5) = 21(1.71)^5 = 21 \times 14.2 = 298.2$ (too high) - (B) $T(5) = 21(0.58)^5 = 21 \times 0.056 = 1.176$ (too low) - (D) $T(5) = 70 - 49(0.69)^{5/5} = 70 - 49(0.69) = 70 - 33.81 = 36.19$ (close to 36) 6. **Evaluate function (D) at $m=10$ and compare to 47°F:** - $T(10) = 70 - 49(0.69)^{10/5} = 70 - 49(0.69)^2 = 70 - 49(0.4761) = 70 - 23.33 = 46.67$ (close to 47) 7. **Conclusion:** Function (D) best models the temperature because it matches initial temperature and closely fits the temperatures at 5 and 10 minutes. **Final answer:** $$T(m) = 70 - 49(0.69)^{\frac{m}{5}}$$