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If the rate of change of the temperature of the inside of an unheated house is proportional to the difference between the internal and external temperatures...
And it is known that, when the internal temperature is 20 degrees (Fahrenheit) hotter than the external temperature, the house cools at a rate of 4 degrees per hour...
And the external temperature can be described by the following function in which t represents time in hours:
f(t)=50+10sin(2*pi*t/24)
And at t=0 it was 6:00 am and the house's heater was shut off while the house was 68 degrees...
What is the function which models the internal temperature at time t, and what time does the internal temperature match the external temperature?
