Question

A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 67°C, it is cooling at a rate of 1°C per minute. When does this occur? Approximate to three decimal places. ...?

Answer 1

let's say the temperature at time t is C(t).at t = 0, C(t) = 95the rate of cooling dC(t)/dt is proportional to the difference in temperature between the coffee and the room.so,
 dC(t)/dt is proportional to C(t)-20at
C(t) = 67
dC(t)/dt = 1 = k*67-20
or
 k = 1/47