1) How much faster does your heart beat when running? Starting with one mile per hour, your heart will beat faster than at rest, so for every mile per hour you run how much faster will your heart beat?

2) How many times will a heart beat after x amount of time if every 10th time it beats, it beats an extra time?

3) If every time I read a page in a book, that number of pages would be added to the end, how many pages will be in the book at after reading x amount of pages?

4) When serving a volleyball, I use one arm to hit the ball, if every time I hit a ball one more arm appears on my existing arm, how many arms will I have after x amount of balls have been hit. (One arm is added to every arm, not just the original.)

Linear: How many times will a heart beat after x amount of time if every 10th time it beats it beats an extra time.

Expodential: How will the answer differ from the answers to the linear function if the answer is squared.

A heart beats 70 times a minute.

M= minutes

Liner:

Rule f(x): [[(70*M)/10] + 70*M]

X Y

1 77

2 154

3 231

In (x)- minutes

Out (y)- beats

Expodential:

Rule f(x): [[(70*M)/10] + 70*M]^2

X Y

1 5929

2 23716

3 53361

In (x)- minutes

Out (y)- beats

First, since I’m dealing with such large numbers, I reduced the number of beats per minute (70) to 10, just so my experiment will be more manageable. To perform my experiment, since it would be physically impossible to make a heart beat an extra time, I used a stress ball to represent a heart, and me squeezing it to represent it beating. Next, I held the ball in my hand and decided x (represent minutes) would be 2. For two minutes I squeezed the ball and every time I reached the tenth beat, I added an extra beat. I recorded how many times and I squeezed the ball and repeated this process for 5 minutes, then 10 minutes, this is my data:

2min- 22 beats

5min- 55 beats

10min- 110 beats

I realized, if my expierment was correct, this data should match with the data from my function table. Finally, to find get the data for the expodential part of the question, I took each number and multiplied it by its self.

It is clear that the data from my first In-Out table is linear because I plotted the points on a graph and the resulting line was linear.

Reflection:

The first Habit of a Mathematician I gained through this project was being confident. When making In-Out function tables, I never second guessed myself and always ended up with the right answer. This strengthened my my knowledge because when I am confident with my work, I helps me be confident with everything involving the project. Another Habit I picked up was being patient and persistent. When developing a formula, I created about three inaccurate rules before I found the correct one, but, since I was patient, I eventually found the correct answer and completed my work. The final Habit I picked up on was being organized. I kept all my work together and the dates that things were due in an organized calendar, this helped me keep on task and not lose anything.

The first thing the guests at my exhibition said was 'whats that?' then pointed to my art piece. It obviously catches the eye, being so colorful and bright, so it caused a lot of math involved interaction. I told everyone who came by about the math part and creative part of the project, and showed them how the heart beats. Everyone who came was very interested in what I had to say and were very impressed about how much I knew about the subject.

The first Habit of a Mathematician I gained through this project was being confident. When making In-Out function tables, I never second guessed myself and always ended up with the right answer. This strengthened my my knowledge because when I am confident with my work, I helps me be confident with everything involving the project. Another Habit I picked up was being patient and persistent. When developing a formula, I created about three inaccurate rules before I found the correct one, but, since I was patient, I eventually found the correct answer and completed my work. The final Habit I picked up on was being organized. I kept all my work together and the dates that things were due in an organized calendar, this helped me keep on task and not lose anything.

The first thing the guests at my exhibition said was 'whats that?' then pointed to my art piece. It obviously catches the eye, being so colorful and bright, so it caused a lot of math involved interaction. I told everyone who came by about the math part and creative part of the project, and showed them how the heart beats. Everyone who came was very interested in what I had to say and were very impressed about how much I knew about the subject.