SOLUTION: The average monthly temperature of a town can be modeled by the function T(t)=14.6sin0.5(t-1)+9.15 where T is the temperature in degrees Celsius and t = 0 represents January 1, t =
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Question 1091295: The average monthly temperature of a town can be modeled by the function T(t)=14.6sin0.5(t-1)+9.15 where T is the temperature in degrees Celsius and t = 0 represents January 1, t = 1 represents February and so on. In which month is the average monthly temperature the highest?
a. March c. May
b. April d. June
Answer by greenestamps(13209) (Show Source): You can put this solution on YOUR website!
The 14.6 and 9.15 only affect the amplitude and the midline of the graph. The "sin(0.5(t-1))" is what determines what values of t give maximum, minimum, or average temperatures.
The sine function has its maximum value when the angle is pi/2. So
So the value of t that gives the maximum average temperature is pi+1, or about 4.14. Since t=0 represents January, 4 represents May. So the highest average monthly temperature is in May.
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