Newton's law of cooling states that the rate of change of temperature of an object in a surrounding medium is proportional to the difference of the temperature of the medium and the temperature of the object. suppose a metal bar, initially at temperature 30 degrees celsius, is placed in a room which is held at the constant temperature of 10 degrees celsius. one minute later the bar has cooled to 10.99574 degrees . write the differential equation that models the temperature in the bar (in degrees celsius) as a function of time (in minutes). hint: you will need to find the constant of proportionality. start by calling the constant k and solving the initial value problem to obtain the temperature as a function of k and t . then use the observed temperature after one minute to solve for k .

dt/dt = 3(10-t) correct: your answer is correct.

so what i got is only dt/dt=k(tm-to)=k(10-to)

can some one explain how do they get the value of k as 3?