**Unit 2 Project - Math II**

Sarah Lamm - Math II - Period 3

# Activity 1: Graphing

In this activity I used a table that showed the sound beats per minute from songs in a mash-up. I graphed the beats per minute as a function of time, and then I found the piecewise function that corresponds to the graph.

### "5 Minute Mash-Up as a Piecewise Function Graph"

The second part of this activity was finding the piecewise function of the graph. What is a piecewise function? A piecewise function is used to graph a relationship of functions. Below is the piecewise function for the graph above.

# Activity 2: Modeling

In this activity I found the average BPM of the 4 songs but I also added a crescendo for the last 2 minutes of the song. Once I gathered my information I created a graph. The average BPM is 121 for all 4 songs

### "5 Minute Mash-Up with Crescendo"

Below if the function for the graph. The y = 122 shows the constant BPM of the song for the first 3 minutes. The y = 121.5 + 5^(x-3) shows the exponential growth of the BPM after the 3rd minute. The number 121.5 is the average of all the songs' BPMs and is where the exponential growth starts at. 5 is part of the parent function which shows the rate of exponential growth and 3 is the horizontal translation.

What is the BPM at....

3 minutes? 123

4 minutes? 126

5 minutes? 146

# Activity 3: Designing

In this activity I have compiled 4 songs and collected their BPM. Now I will create a graph and piecewise function to show my mash-up

### "My 5 Minute Mash-Up Graph"

Below is the piecewise function for the graph of my mash up. Notice that the greater than or equal to signs, as well as the less than or equal to sign correspond to the closed circles on the graph.

Here is the graph of my mashup with a crescendo. This technique averages the BPM of all the songs for the first 3 minutes and then plugs the information into a formula for the last 2 minutes. The formula for this mash-up's crescendo was 132 + 5^ x - 3.