assignment question!! rate of change of temperature?

Question

the rate of change of temperature is with respect to time of a liquid which has been boiled and then allowed to cool is given by

dT / dt = -0.3(T-s)

where T is the temperature at the time t minutes and s is the surrounding temperature. Find the area/s of the region from T = 35 to T = 120 for a variety of surrounding temperatures showing the variation in the graphs and values of the regions. What does the area of the region represent?


please explain :)

Answer 1

separating variables dT/(T-s)= -0.3dt
so lnIT-sI= -0.3t+k
T-s=Ce^-0.3t so
T= s+Ce^-0.3t (to fix C you need To at a time to)
so T is a function of two variables T(s,t).
I don´t understand what area are you asking for.
Please clarify

Answer 2

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Answer 3

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Answer 4

1/(T-s) dT = -0.3dt
Integrate both sides with limits,
ln|(120-s)/(35-s)| = (-0.3t)
Can you finish the remaining parts?