I understand how to differentiate Newton's Law of Cooling to get T, and determine what the general and specific solution for a scenario where the ambient temperature is constant but how do you set up an equation for a room who's temperature fluctuates like below.

03:00 58.9

04:00 58.5

05:00 57.2

06:00 57.6

07:00 57.0

08:00 56.7

09:00 61.5

10:00 65.3

11:00 71.1

The professor suggested using a piece wise function but I am not sure how I should do that. I was thinking making a linear equation from the data but not sure how that would work.