Substitute some value of t into the rule. Do you get values of T that make sense? What happens if you substitute t = 1/2, for example ...? What values of T do you get for odd values of t ....?
Use some mathematical common sense.
Oh, I guess -0.97 wouldn't make sense. It seems as though the temperture fluctuates too wildly.
At 2 hours I came up with: T = 90.6
Then at 3 hours it went to: T = -48.5
Then at 4: T = 86.4
That doesn't make a heck of a lot of sense. Especially when a half hour yields a 'domain error' on my calculator.
So b has to be positive, then...
(And I apologize again. I'm pretty much devoid of mathematical common sense. It's never made any sense to me...)