Suppose the temperature at 12:00 noon is increasing at an (instantaneous)

rate of

3


degrees F. per hour. What is the rate of change of the temperature
in degrees C. per hour.

Hint: The relationship between degrees F. and degrees C. is linear,
zero (0) degrees C

equals 32 degrees F, and 100 degrees C equals 212 degrees F.



The rate of change in degrees C per hour is

rate= 3F/hr= 3(5/9) C/hr

To find the rate of change of the temperature in degrees Celsius per hour, we need to convert the given rate of change in degrees Fahrenheit per hour to degrees Celsius per hour.

The relationship between degrees Fahrenheit (F) and degrees Celsius (C) is given by:

C = 5/9 * (F - 32)

Given that the rate of change in degrees Fahrenheit per hour is 3°F per hour, we can substitute this value into the formula to find the rate of change in degrees Celsius per hour:

C' = 5/9 * (3 - 32)

Simplifying the expression, we have:

C' = 5/9 * (-29)

C' = -145/9

Therefore, the rate of change of the temperature in degrees Celsius per hour is approximately -16.11°C per hour.