A cup of coffee at 85 degrees Celsius is placed in a room at 25 degrees Celsius. Suppose that the coffee cools at a rate of 5 degrees Celsius per minute when the temperature of the coffee is 70 degrees. The differential equation describing this has the form dT/dt = k (T-A)

A= 25

k=?

Either from drawing the direction field (try Maple or by hand) or other intuitive means, the limiting value of T should be = 25

k = - 6.6667

Step-by-step explanation:

this is quite very simple to begin. I would encourage you take other practice questions similar to help with understanding it.

let us begin.

Given that ;

dT/dt = k ( Tm - T)       where Tm is the temp of the medium

dT/dt = 5 degrees Celsius per minute    when T = 70

so we have that, 5 = k ( 25 - 70)

remember to convert 5 degree celsius per minute to seconds

we have that;

5*60(sec) = k ( 25 - 70)  

k = 5*60 / ( 25 - 70)

k = - 6.6667

note K is negative because we consider it for cooling process  (temp decreasing).

cheers i hope this helps!!!