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.
Answers
Given : 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.
To Find : Sinusoidal function
Solution:
y = A sin( kt + c) + h
A = (2,000,000 - 1,000,000) /2 = 500,000
h = (2,000,000 + 1,000,000) /2 = 1,500,000
low to max in 6 month hence cycle = 12 month
2π/k = 12
=> k = π/6
y = 500,000 sin( (π/6)t + c) + 1,500,000
2,000,000 in march t = 3 => (π/6)3 = π/2
=> 2,000,000 = 500,000 sin( π/2 + c ) + 1,500,000
=> 500,000 = 500,000 sin( π/2 + c )
=> 1 = sin( π/2 + c )
=> sin( π/2 ) = sin( π/2 + c )
=> c = 0
y = 500,000 sin( tπ/6) + 1,500,000
y = number of visitors and t is number of month
Learn More:
The depth of water in a harbour varies as a function of time. The ...
https://brainly.in/question/33746750