Start with an initial temperature of T0 = 70° at t = 0 hours, and add to that a sine function that does the following, in order:
Rises by 10°, reaching 80° after 6 hours
Drops by 10º, reaching 70° after 12 hours
Drops by 10°, reaching 60° after 18 hours
Rises by 10°, reaching 70° after 24 hours
Note that the amplitude of the sine function is A = 10°.
T = period of the sine function
T = 24 hours
f(x) = T0 + A sin[(2π/T)x]
where
T0 = 70°
A = 10°
T = 24 hours
x = elapsed time in hours
f(x) = 70º + (10°)sin[(π/12)x]
with x in hours.
Test this solution and see that it fits the data. (Make sure your calculator is in the radian mode!)
