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Attendance at a state park throughout the year is found to be periodic and can be modeled by a
sine function. The attendance ranges from a low of approximately 1,000,000 visitors in September
to a high of approximately 2,000,000 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?

N(t) = 1.5 sin(t) + 0.5

N(t) = 0.5 sin(t) +1.5

N(t) = 2 sin ( ₹t) – 1

N(t) 0.5 sin(2t) + 1.5

Respuesta :

The sin function can be model as N(t) = 0.5sin(Ï€t/6) + 1.5 if the attendance ranges from a low of approximately 1,000,000 visitors in September to a high of approximately 2,000,000 visitors in March.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

The attendance ranges from a low of approximately 1,000,000 visitors in September to a high of approximately 2,000,000 visitors in March.

We know the sine function is:

y = Asin(w + c) + s

Here:

A is amplitude

w is angular velocity,

s is vertical Displacement,

c = phase angle

A = (2000000 - 1000000) /2 =  500,000

w = 2π/T  

T = 12

w = 2π/12 = π/6

s = (1000000 +2000000) /2 = 3,000,000/2 = 1,500,000

500,000sin(Ï€/6 + 0) + 1500000

500000sin(Ï€/6)+1500000

or

0.5sin(Ï€t/6) + 1.5

Thus, the sin function can be model as N(t) = 0.5sin(Ï€t/6) + 1.5 if the attendance ranges from a low of approximately 1,000,000 visitors in September to a high of approximately 2,000,000 visitors in March.

Learn more about the function here:

brainly.com/question/5245372

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