Question

consider a 38 degree F object placed in 68 F room write a differential equation for T thetemperature of the object at time t using k>0 for the constant of proportionality and write your equation in terms of T k and t

Answer 1

dY/dt = k(Y - Ys).

Step-by-step explanation:

Okay, this question based on the law known as the Newton's law of cooling. According to Newton's law of cooling, when an object is placed into a specific or particular environment, the object's temperature will definitely be lower than the temperature of the surrounding or the environment.

So, we are given that the temperature of the object = 38 degree F = Y(o) of the object and the temperature of the environment = 68 degree F = Ys

Hence, dY/dt = k(Y - Ys).

dY/ (Y - Ys) =kdt.