AnswersAlgebra 2 MP 234 CHSThe Unit Circle

Modeling with Periodic Functions Answers

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The height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds can be modeled by the equation . What is the period of the function?

Question illustration
A
seconds
Option A
B
seconds
Option B
C
8 seconds
D
20 seconds
2
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A buoy starts at a height of 0 in relation to sea level and then goes up. Its maximum displacement in either direction is 6 feet, and the time it takes to go from its highest point to its lowest point is 4 seconds. Which of the following equations can be used to model h, the height in feet of the buoy in relation to sea level as a function of time, t, in seconds?

A
h = 4 sine (StartFraction pi Over 6 EndFraction t)
Option A
B
h = 4 sine (StartFraction pi Over 3 EndFraction t)
Option B
C
h = 6 sine (StartFraction pi Over 4 EndFraction t)
Option C
D
h = 6 sine (StartFraction pi Over 2 EndFraction t)
Option D
3

The height, d, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation . The ball is released from its lowest point at seconds. Using your knowledge of the general form of sine and cosine functions, which of the following equations can also model this situation?

Question illustration
A
d = negative 2 cosine (pi t) + 5
Option A
B
d = negative 2 cosine (pi (t + one-half)) + 5
Option B
C
d = 2 cosine (pi t) + 5
Option C
D
d = 2 cosine (pi (t + one-half)) + 5
Option D
4

Mark sits on a swing that is 2.5 feet off the ground. Swinging as hard as he can, the swing reaches a height of 6 feet. Assuming Mark holds a steady pace, the height of the swing could be represented by a cosine curve.If Mark makes a full swing forward and backward in 3 seconds, which graph below could represent the height of the swing, in feet, for any time, t?

A
On a coordinate plane, seconds is on the x-axis and feet is on the y-axis. A curve starts at (0, 3). It has a maximum of y = 6 and a minimum of y = 3. It goes through 1 cycle in 1.5 seconds.
Option A
B
On a coordinate plane, seconds is on the x-axis and feet is on the y-axis. A curve starts at (0, 3). It has a maximum of y = 8 and a minimum of y = 4. It goes through 1 cycle in 1.5 seconds.
Option B
C
On a coordinate plane, seconds is on the x-axis and feet is on the y-axis. A curve starts at (0, 3). It has a maximum of y = 6 and a minimum of y = 3. It goes through 1 cycle in 3 seconds.
Option C
D
On a coordinate plane, seconds is on the x-axis and feet is on the y-axis. A curve starts at (0, negative 2). It has a maximum of y = 2 and a minimum of y = negative 2. It goes through 1 cycle in 1.5 seconds.
Option D
5

The distance, d, in inches of a weight attached to a spring from its equilibrium as a function of time, t, in seconds can be modeled by the graph below. Which equation is represented in the graph below?

Question illustration
A
d = negative 10 cosine (StartFraction pi Over 2 EndFraction t)
Option A
B
d = negative 10 cosine (pi t)
Option B
C
d = negative 5 cosine (StartFraction pi Over 2 EndFraction t)
Option C
D
d = negative 5 cosine (pi t)
Option D
6

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
7

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
8

The displacement, d, in millimeters of a tuning fork as a function of time, t, in seconds can be modeled with the equation . What is the maximum displacement of the tuning fork?

Question illustration
A
0.2 mm
B
0.4 mm
C
0.8 mm
D
2.5 mm

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