Math II Unit 2 Project: Modeling Mashups

Activity One

1. Graph the data from the table. (Table is included with graph).

Table from Activity 1, along with its graph

2. Next, write a function that represents the graph. What type of function is it?

The colors correspond with the table colors.

--The functions are all piecewise functions.

Activity 2

1. Determine the tempo for 0<x<3 by finding the average BPM of all four sound bites. What is the average? Round your answer to the nearest whole number.

--The average tempo of the four songs above rounds to 122.

2. The tempo for 3≤x≤5 is modeled by the function y=121+5^(x-3). Using your knowledge of transformations, write a brief summary telling how the graph of y compares to the graph of its parent function. Include a discussion of what the numbers "121," "5," and "-3" mean in terms of this activity.

--Compared to its parent function, y=5^x, the graph is raised by 121, because that number acts as k, which moves the graph along the y-axis. The number 5 is greater than one, so it ensures that the graph is a growth. The number -3 shifts the graph horizontally to the right.

3. Graph the finished mashup.

--(Pictured below)

4. Write a function that represents the graph.

--y=121, 0≤x<3 and

y=121+5^(x-3), 3≤x≤5

5. What is the BPM when the song reaches 3.5 minutes? 4 minutes? 5 minutes?

--At 3.5 minutes, the BPM reaches to 123.24.

--At 4 minutes, it raises to 126 BPM.

--At 5 minutes, the BPM is 146.

Activity 3

Now it's your turn to start a mashup. Choose 4 songs to create a 5-minute

mashup, and follow the steps you used in Activities 1 and 2.

1. Graph your mashup and write the piecewise function

representing the graph.

The songs I chose for my own mashup.

The function to represent this graph is a piecewise function:

1. Determine the tempo for 0<x<3 by finding the average BPM of all four sound bites. What is the average? Round your answer to the nearest whole number.

--The average tempo to the four sounds I chose round to 104.

2. The tempo for 3≤x≤5 is modeled by the function 103+5^(x-3). Using your knowledge of transformations, write a brief summary telling how the graph of y compares to the graph of its parent function. Include a discussion of what the terms "103," "5," and "-3" mean in terms of this activity.

--Compared to its parent function, the graph of 103+5^(x-3) is raised by 103 units up the y-axis, because that number serves as k. The number 5 is b, and it is positive, which makes the exponential graph a growth. The graph also moves horizontally to the right because of -3, which is h.

3. Graph the finished mashup.

The finished mashup with a crescendo.

4. Write a function that represents the graph.

--y=103, 0≤x<3 and

y=103+5^(x-3), 3≤x≤5

5. What is the BPM when the song reaches 3.5 minutes? 4 minutes? 5?

--At 3.5 minutes, the song reaches 105.24 BPM.

--At 4, it reaches 108.

--At 5, the BPM is at 128.

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