Suppose you have just poured a cup of freshly brewed coffee with temperature 95°C in a room where the temperature is 20°C. Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Therefore, the temperature of the coffee, T(t), satisfies the differential equation dT = k(T – Troom) - dt where Troom temperature, and k is some constant. Suppose it is known that the coffee cools at a rate of 1°C per minute when its temperature is 70°C. 20°C is the room A. What is the limiting value of the temperature of the coffee? lim T(t) = B. What is the limiting value of the rate of cooling? dT lim dt C. Find the constant k in the differential equation. k =

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.