Answer:
[tex] T'(t)=k(M(t)-T(t))[/tex]
Step-by-step explanation:
The rate of change in the temperature T of coffee at time t is written as [tex]T'(t)[/tex] (remember derivatives are used to express rates of change, and in our case the rate of change of the temperature T). The difference between the temperature M of the air at time t, and the temperature T of the coffee at time t can be expressed as [tex]M(t)-T(t)[/tex]
Saying that the rate of change in the temperature T is proportional to the difference between M and T is just a way of saying that the rate of change in the temperature T is equal to the difference between M and T, multiplied by some constant k (whose value we don't know, but still that's what it means).
Therefore we get
[tex] T'(t)=k(M(t)-T(t))[/tex]
