Question 1181064: Mr. Wong has noticed a whole lot of sneezing in his class in a past few years. He has investigated the situation and has gathered some information.
• The highest percent of the population suffering from allergies is 20% and it happens in May
• The lowest percent of the population suffering from allergies is 10% and it happens in November
• The pattern repeats yearly (every 12 months)
Let P be the percent of the population suffering from allergies and t be time in months after January (i.e.January is when t = 0), determine an equation that models this situation. (this is about sinusoidal functions)
Answer by ikleyn(52903)   (Show Source):
You can put this solution on YOUR website! .
I will use the cosine function.
The middle level is P = 0.15, and the amplitude is 0.05, obviously.
So, I write P(t) = 0.15 + 0.05*cos(2pi*x).
The starting value for the factor "x" is 0 at t= 5 ( x must be 0 at May ), and the period is 12 months (one year).
So, I take x =  , and then my final formula is
P(t) =  , ANSWER
where t is the index showing the month of the year. For clarity, t = 5 for May.
Solved, answered and carefully explained.
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