AnswersCommon Core Algebra II - MA3111 B-ICModeling with Periodic Functions

Modeling with Periodic Functions Answers

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1
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Which of the following situations can be modeled with a periodic function?

A
the height of a football after it has been thrown
B
the height of a person riding on an escalator
C
the height of a building after it has been constructed
D
the height of a pebble stuck in the tread of a tire
2
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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
3

Tides in a specific location can be approximated using the periodic function shown on the graph.What is the interpretation of the amplitude in this application?

Question illustration
A
the time between high tides
B
the time between high tide and low tide
C
the sum of the heights at high tide and low tide
D
the distance halfway between the height at high tide and low tide
4

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
5

The equation can be used to model the height, h, in feet of the end of one blade of a windmill turning on an axis above the ground as a function of time, t, in seconds. How long is the blade? Assume that the blade is pointing to the right, parallel to the ground, at t = 0, and that the windmill turns counterclockwise at a constant rate.

Question illustration
A
7 feet
B
14 feet
C
21 feet
D
28 feet
6

The height, h, in feet of the tip of the minute hand of a wall clock as a function of time, t, in minutes can be modeled by the equation . Which number (from 1 to 12) is the minute hand pointing to at t = 0?

Question illustration
A
3
B
6
C
9
D
12
7

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
8

Starting at its rightmost position, it takes 2 seconds for the pendulum of a grandfather clock to swing a horizontal distance of 18 inches from right to left and 2 seconds for the pendulum to swing back from left to right. Which of the following equations models d, the horizontal distance in inches of the pendulum from the center as a function of time, t, in seconds? Assume that right of center is a positive distance and left of center is a negative distance.

A
d = 9 cosine (StartFraction pi Over 4 EndFraction t)
Option A
B
d = 9 cosine (StartFraction pi Over 2 EndFraction t)
Option B
C
d = 18 cosine (StartFraction pi Over 4 EndFraction t)
Option C
D
d = 18 cosine (StartFraction pi Over 2 EndFraction t)
Option D
9

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
10

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
11

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
12

A driver runs over a nail, puncturing the tire without causing a leak. The position of the nail in the tire, with relation to the ground, while the car is moving at a constant speed is shown in the table. Time (s)Approximate height of the nail off the ground (inches)000.012.10.027.60.0314.90.0421.50.0525.50.0625.50.0721.5Which key feature of the function representing the nail’s travel can be used to determine the amount of time it takes for the nail to reach the same orientation it had when it entered the tire?

A
period
B
minimum
C
maximum
D
amplitude
13

Suppose that you want to model the height of a rider on a Ferris wheel as a function of time, t, in minutes. If the rider is at the bottom of the Ferris wheel at t = 0 minutes, which of the following would be easiest to use?

A
the cosine function unreflected
B
the sine function unreflected
C
the cosine function reflected about its midline
D
the sine function reflected about its midline
14

The height, h, in feet of a buoy in relation to sea level as a function of time, t, in seconds can be modeled by the graph below. How long does it take for the buoy to go from its highest point to its lowest point and then back to its highest point?

Question illustration
A
1 second
B
2 seconds
C
3 seconds
D
4 seconds
15

The equation models the horizontal distance, d, in inches of the pendulum of a grandfather clock from the center as it swings from right to left and left to right as a function of time, t, in seconds. According to the model, how long does it take for the pendulum to swing from its rightmost position to its leftmost position and back again? Assume that right of center is a positive distance and left of center is a negative distance.

Question illustration
A
0.625 seconds
B
0.8 seconds
C
1.25 seconds
D
1.6 seconds

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