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Suppose the rate of change of the temperature of a body is proportional to the difference...

Suppose the rate of change of the temperature of a body is proportional to the difference between & the temperature of the body and the temperature of the surrounding environment which is 35 . The k initial body temperature is 120 After 40 minutes, the temperature went to 60 .

a.) Find the differential equation with initial condition that models this situation.

b.) Solve to find the general solution using the technique of separation of variables. Call the constant C

c.) Use the initial condition to help find the constant C

d.) Use the fact that to find the value of the constant of proportionality k

e.) After how long will the temperature be 39 ?

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