## The differential equation below models the temperature of a 85 degree C cup of coffee in a 25 degree C room, where it is know that the coffe

Question

The differential equation below models the temperature of a 85 degree C cup of coffee in a 25 degree C room, where it is know that the coffee cools at a rate 1 degree C per minute when its temperature is 75 degree C. Solve the differential equation to find an expression for the temperature of the coffee at time t. (Let y be the temperature of the cup of coffee in degree C, and let t be the time in minutes, with t = 0 corresponding to the time when the temperature was 85 degree C.) dy/dt = -1/50(y-25)

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1 week 2021-09-10T22:48:28+00:00 1 Answer 0

Step-by-step explanation:

We are given that differential equation

We have to find the expression for the temperature of the coffee at time t.

Let y be the temperature of the coffee in degree C and t be the time in minutes.

At t=0 , y=85 degree Celsius

Integrating on both sides

Substitute the value t=0 and y=85 then we get

Substitute the value of C

Then , we get

This is required expression for the temperature of the coffee at time t.