1.

+ -/2 points

My Notes

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 40 degrees Celsius, is placed in a room which is held at the constant temperature of 30 degrees Celsius. One minute later the bar

has cooled to 30.49787 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

Now write a formula for the solution T(t) with initial temperature 7(0)=40 .

T(t) =