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A cup of hot coffee has been left to cool in a room with an ambient temperature of 21^(@)C. The relationship between the elapsed time, m, in minutes, since the coffee was left to cool, and the temperature of the coffee, T, measured in ^(@)C, is modeled by the following function. T(m)=21+74*10^(-0.03 m) What will the temperature of the coffee be after 10 minutes? Round your answer, if necessary, to the nearest hundredth. ^(@)C

A cup of hot coffee has been left to cool in a room with an ambient temperature of 21∘C 21^{\circ} \mathrm{C} .\newlineThe relationship between the elapsed time, m m , in minutes, since the coffee was left to cool, and the temperature of the coffee, T T , measured in ∘C { }^{\circ} \mathrm{C} , is modeled by the following function.\newlineT(m)=21+74⋅10−0.03m T(m)=21+74 \cdot 10^{-0.03 m} \newlineWhat will the temperature of the coffee be after 1010 minutes?\newlineRound your answer, if necessary, to the nearest hundredth.\newline∘C { }^{\circ} C

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Q. A cup of hot coffee has been left to cool in a room with an ambient temperature of 21∘C 21^{\circ} \mathrm{C} .\newlineThe relationship between the elapsed time, m m , in minutes, since the coffee was left to cool, and the temperature of the coffee, T T , measured in ∘C { }^{\circ} \mathrm{C} , is modeled by the following function.\newlineT(m)=21+74⋅10−0.03m T(m)=21+74 \cdot 10^{-0.03 m} \newlineWhat will the temperature of the coffee be after 1010 minutes?\newlineRound your answer, if necessary, to the nearest hundredth.\newline∘C { }^{\circ} C
  1. Identify Function and Value: Identify the given function and the value to be substituted.\newlineThe function given is T(m)=21+74×10(−0.03m)T(m) = 21 + 74 \times 10^{(-0.03m)}, where mm is the elapsed time in minutes. We need to find the temperature of the coffee after 1010 minutes.
  2. Substitute Value into Function: Substitute the value of mm into the function.\newlineWe substitute m=10m = 10 into the function to find T(10)T(10).\newlineT(10)=21+74×10(−0.03×10)T(10) = 21 + 74 \times 10^{(-0.03 \times 10)}
  3. Calculate Exponent: Calculate the exponent part of the function.\newlineCalculate 10(−0.03×10)10^{(-0.03 \times 10)} which is 10(−0.3)10^{(-0.3)}.\newline10(−0.3)≈0.501187233610^{(-0.3)} \approx 0.5011872336
  4. Multiply with 7474: Multiply the result of the exponent with 7474. Multiply 7474 by the result from the previous step. 74×0.5011872336≈37.087860889674 \times 0.5011872336 \approx 37.0878608896
  5. Add to Find T(10)T(10): Add 2121 to the result from the previous step to find T(10)T(10).\newlineT(10)=21+37.0878608896T(10) = 21 + 37.0878608896\newlineT(10)≈58.0878608896T(10) \approx 58.0878608896
  6. Round to Nearest Hundredth: Round the result to the nearest hundredth.\newlineRound 58.087860889658.0878608896 to the nearest hundredth.\newlineT(10)≈58.09∘CT(10) \approx 58.09^{\circ}C

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