12 **Newton's Law of Cooling: Average Temperature Calculation****Problem Statement:**If a cup of coffee has a temperature of 93°C in a room where the ambient air temperature is 20°C, then, according to Newton's Law of Cooling, the temperature of the coffee after \( t \) minutes is given by:\[ T(t) = 20 + 73e^{-\frac{t}{55}} \]**Question:**What is the average temperature of the coffee during the first 26 minutes?**Solution:**To find the average temperature, you will need to calculate the definite integral of the temperature function \( T(t) \) over the interval from \( t = 0 \) to \( t = 26 \) and then divide by the length of the interval (26 minutes).**Formula:**\[ \text{Average Temperature} = \frac{1}{26} \int_{0}^{26} \left( 20 + 73e^{-\frac{t}{55}} \right) dt \]Please input the average temperature calculation in the box provided:\[ \text{average temp} = \_\_\_\_ \text{°C} \]**Graphical Representation:**While not provided here, a possible graph to accompany this explanation would illustrate the exponential decay curve of the coffee's temperature over time, starting at 93°C and approaching 20°C as time increases. This visualization helps to understand how the temperature changes dynamically.To calculate the average, you would use integral calculus techniques, which provide a precise way to determine the mean value of such non-linear functions over specified intervals.

According to the questionCup of coffee has temperature 93°C in a room where the ambient air…

If a cup of coffee has temperature 93°C in a room where the ambient air temperature is 20°C, then, according to Newton's Law of Cooling, the temperature of the coffee after t minutes is T(t) = 20 +73e-t/55 What is the average temperature of the coffee during the first 26 minutes? average temp = . °C