Respuesta :
Answer:
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, [tex]N(t)_{min}[/tex] = 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
