A covered mug of coffee originally at 200 degrees Fahrenheit, if left for t hours in a room whose temperature is 65 degrees, will cool to a temperature of $65 + 135e^{-1.9t}$ degrees. Find the temperature of the coffee after the following amounts of time. (Round your answers to the nearest degree.) (a) 45 minutes (b) half an hour
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The formula for this is: \[ \frac{dT}{dt} = k(T - T_{room}) \] where: - \( \frac{dT}{dt} \) is the rate of change in temperature - \( k \) is the constant of proportionality - \( T \) is the temperature of the object - \( T_{room} \) is the temperature of the Show more…
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