Newton's law of cooling says that the rate of cooling of an object is
proportional to the difference between the temperature of the object
and that of its surroundings (provided the difference is not too large).
If T=T(t) represents the temperature of a (warm) object at time t, A represents the ambient (cool) temperature, and k is a negative constant of proportionality, which equation(s) accurately characterize Newton's law?
A. dT/dt=kT(T-A) B. dT/dt=k(T-A) C. dT/dt=k(A-T) D. dT/dt=kT(1-T/A) E. All of the above
F. None of the above

B

The work

22

Newton's law of cooling states that the temperature of an
object changes at a rate proportional to the difference between its
temperature and that of its surroundings. Suppose that the temperature
of a cup of coffee obeys Newton's law of cooling. If the coffee has
a temperature of 205 degrees Fahrenheit when freshly poured, and 2.5 minutes later has cooled to 194 degrees in a room at 66 degrees, determine when the coffee reaches a temperature of 164 degrees.
The coffee will reach a temperature of 164 degrees in
minutes.

A thermometer is taken from a room where the temperature is 19ºC to the outdoors, where the
temperature is 1ºC. After one minute the thermometer reads 12ºC.
(a) What will the reading on the thermometer be after 2 more minutes?
,
(b) When will the thermometer read 2ºC?
minutes after it was taken to the outdoors.

A curve passes through the point (0,8) and has the property that the slope of the curve at every point P is
twice the y-coordinate of P. What is the equation of the curve?
y(x)=

8e^(2*x)

The work

25.

Water leaks from a vertical cylindrical tank through a small hole in
its base at a rate proportional to the square root of the volume of
water remaining. The tank initially contains 175 liters and 18
liters leak out during the first day.

A. When will the tank be half empty? t= days

B. How much water will remain in the tank after 5 days?
volume = Liters