Consider a 92∘C cup of coffee placed in a 24∘C room. Suppose it is known that the coffee cools at a rate of 2∘C/min when it is 70∘C. Then according to Newton's law of cooling, the temperature T(t) of the coffee t minutes after being placed in the room satisfies the differential equation,

Question

Consider a 92∘C cup of coffee placed in a 24∘C room. Suppose it is known that the coffee cools at a rate of 2∘C/min when it is 70∘C. Then according to Newton's law of cooling, the temperature T(t) of the coffee t minutes after being placed in the room satisfies the differential equation,
dT/dt=(2/(70−24))(24−T).
What is the temperature (in Celcius) of the coffee at time t=1 min?

I tried a few methods but I am completely stumped with this questions. Can someone please show me steps on how to do it

Damon · Answer

They gave you the hint "Newton's Law of Cooling" so you do not even have to do the calculus. for example: http://www.softschools.com/formulas/physics/newtons_law_of_cooling_formula/93/