Question

The rate of change in the temperature T of coffee at time t is proportional to the difference between the temperature M of the air at time t and the temperature of the coffee at time t.Write a differential equation that fits the above description.

Answer 1

Answer:

$T'(t)=k(M(t)-T(t))$

Step-by-step explanation:

The rate of change in the temperature T of coffee at time t is written as $T'(t)$ (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 $M(t)-T(t)$

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

$T'(t)=k(M(t)-T(t))$