AnswersAlgebra 2 MP 234 CHSModeling with Periodic Functions

Modeling with Periodic Functions Answers

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Blood pressure can be modeled by a sinusoidal curve, where the maximum and minimum on the curve correlate to the person’s blood pressure reading. Henry’s blood pressure is modeled by the function , where t is time in seconds.Which graph accurately depicts this model?

Question illustration
A
On a coordinate plane, seconds is on the x-axis and blood pressure is on the y-axis. A curve starts at (0, 100). It has a maximum of y = 130 and a minimum of y = 70. It goes through one cycle in 1 second.
Option A
B
On a coordinate plane, seconds is on the x-axis and blood pressure is on the y-axis. A curve starts at (0, 100). It has a maximum of y = 130 and a minimum of y = 70. It goes through one cycle in 2 seconds.
Option B
C
On a coordinate plane, seconds is on the x-axis and blood pressure is on the y-axis. A curve starts at (0, 0). It has a maximum of y = 30 and a minimum of y = negative 30. It goes through one cycle in 1 second.
Option C
D
On a coordinate plane, seconds is on the x-axis and blood pressure is on the y-axis. A curve starts at (0, 30). It has a maximum of y = 60 and a minimum of y = negative 0. It goes through one cycle in 1 second.
Option D
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Throughout the day, the depth of water at the end of a dock varies with the tides. The function represents the height, in feet, of the water t hours after midnight.Which graph shows the height of the water at the dock at any time after midnight?

Question illustration
A
On a coordinate plane, feet is on the x-axis and depth is on the y-axis. A curve starts at (0, 5). It decreases through the y-axis. It has a minimum of y = 2 and a maximum of y =12. It goes through 1 cycle in 13 feet.
Option A
B
On a coordinate plane, feet is on the x-axis and depth is on the y-axis. A curve starts at (0, 5). It increases through the y-axis. It has a minimum of y = 2 and a maximum of y =12. It goes through 1 cycle in 13 feet.
Option B
C
On a coordinate plane, feet is on the x-axis and depth is on the y-axis. A curve starts at (0, 5). It increases through the y-axis. It has a minimum of y = 2 and a maximum of y =12. It goes through 1 cycle in 7 feet.
Option C
D
On a coordinate plane, feet is on the x-axis and depth is on the y-axis. A curve starts at (0, negative 2). It increases through the y-axis. It has a minimum of y = negative 5 and a maximum of y =5. It goes through 1 cycle in 13 feet.
Option D
3

A rider boards a Ferris wheel 10 feet above ground level. The diameter of the Ferris wheel is 50 feet and the wheel completes one full rotation every 24 seconds. Which graph represents the relationship between time and height off the ground?

A
On a coordinate plane, a curve starts at (0, 10). It has a maximum at y = 60 and a minimum at y = 10. It increases through the y-axis. Its cycle is 0.4 x.
Option A
B
On a coordinate plane, a curve starts at (0, 60). It has a maximum at y = 60 and a minimum at y = 10. It decreases through the y-axis. Its cycle is 0.4 x.
Option B
C
On a coordinate plane, a curve starts at (0, 10). It has a maximum at y = 60 and a minimum at y = 10. It increases through the y-axis. Its cycle is 0.8 x.
Option C
D
On a coordinate plane, a curve starts at (0, 10). It has a maximum at y = 60 and a minimum at y = 10. It decreases through the y-axis. Its cycle is 0.8 x.
Option D
4

Suppose that you want to model the height of a rider on a Ferris wheel as a function of time. The amplitude of the function you use as a model should be equal to which of the following?

A
the area of the Ferris wheel
B
the circumference of the Ferris wheel
C
the diameter of the Ferris wheel
D
the radius of the Ferris wheel

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