Question 1035429: The temperature at, T (degrees Celsius), inside a building on given day is given by the function:
T= 8sin pi(little t)/8 +18
where little t is the number of hours after 8am.
a) What is the maximum temperature in the building and the time at which it occurs?
b) Find the temperature at i) 11am, ii) 6pm, iii) 12am (midnight).
c) For how long is the temperature below 15 degrees?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
The key to this problem is to be able to calculate the period of the function from the coefficient on the input variable, in this case  .
In general, the period of a periodic function is the period of the function with an unmodified variable divided by the absolute value of the coefficient on the variable. Since the period of ) is  , the period of ) is  .
In your case, the coefficient is  so the period is  .
The lead coefficient, 8, is the amplitude, that is the maximum variation from the midline value, 18. So your function value varies from 10 to 26.
The rest of your questions can be answered from inspection of the graph:
 .
The mathematics behind this analysis is fairly straightforward and had the question simply posed the function without trying to make the function into a model of a real-world situation, then this would have been rather unremarkable. However, trying to model a daily (i.e. 24-hour periodicity) phenomenon with a 16-hour periodicity model makes me wonder whether the person who wrote the problem is capable of using their head for anything besides a hat rack. If I were you, I would complain -- loudly.
One of the most under-taught skills in mathematics education is the ability to discern whether answers obtained by formulaic processes make sense. And when a posited model of a real-world situation doesn't fit with our understanding of real life, then the ability to get an intuitive sense of the correctness of the answers is destroyed. 50F at 8pm and 79F at 4am is simply nonsense in any real world scenario that I can imagine. This problem is simply stupid.
John
My calculator said it, I believe it, that settles it
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