Attendance at state park throughout the year is found to be periodic and can be modeled by a sine function. The attendance ranges from a low approximately 1,00,000 visitors in september to a high of approximately 2,00,000 visitors in march. If t is the month number, where t=1 is january, and N(t)is the attendance, in millions, of visitors, which of the functions can be used to model this behavior A: N(t)=0.5sin(π/6 t)+1.5 B: N(t)=1sin(π/6 t)-1 C: N(t)=0.5sin(2πt)+1.5 D: N(t)=1.5sin(π/6 t)+0.5

A. N(t) = 0.5·sin((π/6)·t) + 1.5

Step-by-step explanation:

The given parameters are;

The model of the periodic function = Sine function

The low of the attendance = 1,000,000

The month of the low in attendance = September

The high in attendance = 2,000,000

The month number = t,

The month of January is represented by, t = 1

N(t) = The attendance in millions of visitors

The generic sine function which is given as y = a·sin(b·x + c) + d, ranges from -1 to 1

Period = 12 = 2·π/b

∴ b = 2·π/12 = π/6

c = 0

a = The amplitude = (The maximum - The minimum)/2 = (2,000,000 - 1,000,000)/2 = 500,000

Therefore, a = 0.5×1,000,000 = 0.5·N(t)

Therefore, given that the minimum, = 1, we have;

For sin(b·x + c) = -1, a·sin(b·x + c) = -0.5, for the minimum of 1,000,000 = 1 × 1,000,000, we have;

a·sin(b·x + c) + d = 1

∴ -0.5 + d = 1

d = 1.5

Therefore, we have;

N(t) = 0.5·sin((π/6)·t) + 1.5

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step-by-step explanation:

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