Mathematics, 17.06.2020 16:57 izzy201995
If a cup of coffee has temperature 97°C in a room where the ambient air temperature is 25°C, then, according to Newton's Law of Cooling, the temperature of the coffee after t minutes is T ( t ) = 25 + 72 e − t / 45 . What is the average temperature of the coffee during the first 22 minutes?
Answers: 3
![T(t) = 25 + 72 e^{[-\frac{t}{45} ]}](/tpl/images/0687/8662/d819a.png)
minutes is mathematically evaluated as ![T_{a} = \frac{1}{22-0} \int\limits^{22}_{0} {25 +72 e^{[-\frac{t}{45} ]}} \, dx](/tpl/images/0687/8662/ee4f2.png)
![T_{a} = \frac{1}{22} [25 t + 72 [\frac{e^{[-\frac{t}{45} ]}}{-\frac{1}{45} } ] ] \left| 22} \atop {0}} \right.](/tpl/images/0687/8662/78cc3.png)
![T_{a} = \frac{1}{22} [25 t - 3240e^{[-\frac{t}{45} ]} ] \left | 45} \atop {{0}} \right.](/tpl/images/0687/8662/95155.png)
![T_{a} = \frac{1}{22} [25 (22) - 3240e^{[-\frac{22}{45} ]} - (- 3240e^{0} )]](/tpl/images/0687/8662/6be29.png)
![T_{a} = \frac{1}{22} [550 - 1987.12 + 3240]](/tpl/images/0687/8662/2357a.png)
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If a cup of coffee has temperature 97°C in a room where the ambient air temperature is 25°C, then,...
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