Isaac Newton observed that the temperature (in degrees Fahrenheit) of his morning brew (F) changes at a rate that is directly proportional to the difference between the temperature of coffeee and the temperature of the environment. Let m represent the number of minutes. It is also noted by Isaac that his Nest thermostat shows that it is set to a chilly 65 degrees Fahrenheit. (a) Show all work/integration/algebra to set up the differential equation that models this situation and show all work to find the explicit solution to the DE. (b) If Isaac’s coffee comes from the pot at a blazing temperature of 130 degrees and that the coffee has cooled to 99 degrees in 2 minutes, show all work to find the model that relates the temperature of INew’s cup of java, F, to the elapsed minutes, m. (c) Use your model from part (b) to find the time that it will take for I’s coffee to decrease to a more drinkable 75 degrees.
Isaac Newton observed that the temperature (in degrees Fahrenheit) of his morning brew (F) changes at a rate that is directly proportional to the difference between the temperature of coffeee and the temperature of the environment. Let m represent the number of minutes. It is also noted by Isaac that his Nest thermostat shows that it is set to a chilly 65 degrees Fahrenheit.
(a) Show all work/
(b) If Isaac’s coffee comes from the pot at a blazing temperature of 130 degrees and that the coffee has cooled to 99 degrees in 2 minutes, show all work to find the model that relates the temperature of INew’s cup of java, F, to the elapsed minutes, m.
(c) Use your model from part (b) to find the time that it will take for I’s coffee to decrease to a more drinkable 75 degrees. Show all work
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