What is the right choice for question 27) ?

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The general form for the cosine function is y=acos(b(x-h))+k. a gives the amplitude (vertical stretch), b gives the horizontal stretch, h is a horizontal translation (phase shift), and k gives the vertical shift (the midline.)

Given: max=6.4,min=3.6, period is 12.4 hours (time from max to min is 6.2 hours), and the phase shift is 4.5 hours. (Cosine begins at the maximum -- the model has a maximum 4.5 hours after midnight.)

a: `a=("max"-"min")/2=(6.4-3.6)/2=1.4`

b: `b=(2pi)/p` where p is the period: `b=(2pi)/12.4`

h: h=4.5

k: `k=("max"+"min")/2=(6.4+3.6)/2=5`

The formula is `y=1.4cos2pi((t-4.5)/12.4)+5`

This is choice (c).

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