We used the equation y=3^-x and tried to graph the points on paper by first filling out a data table and then raising the Y axis number on the graph by 15 each time. When X was positive, Y was less than 1, and when X was negative, Y was much greater than one. The distances between the points increased quite rapidly, so it was difficult to graph the numbers, as there was a big difference between each. This activity helped me to see the relationship between the positive and negative exponents.
When compared, we noticed that group #5’s graph is the exact opposite of ours, as theirs is positive (y=3^x) and ours is negative (y=3^-x). The graph was flipped on the y axis, but other than that, all the numbers on the Y axis were the same (just in different/opposite order).
The number I researched is called e, but also known as 2.71828…(and so on). It was discovered by a Swiss mathematician, Leonhard Euler in the 1720’s and is now one of the most important numbers to exist, it can be found in anything. E is used in subjects such as calculus, some of probability, and can even help with the study of distribution of prime numbers, which we are learning this semester.
It is the base of natural algorithms and its value is equal to 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + 1/5! + 1/6! + 1/7! + etc… (! meaning factorial). It is just as useful as the number PI and a pretty great thing to know about/research.
Source(s):
http://mathforum.org/dr.math/faq/faq.e.html
http://www.mathsisfun.com/numbers/e-eulers-number.html
- How does gum stretchability relate to bubble size?
It doesn’t because even though Gum A formed a bigger bubble (for both groups), it was, in our experience, about 10 times shorter, when stretched, than Gum B.
2. 5 variables that may affect outcome;
- Amount of each gum (A and B)
- Amount of air/how quickly you blow into bubble
- Number of chews
- Time which each piece of gum layer out before chewing
- Loss of substance (gum B stuck to the outside of mouth during procedure)
- Mouth structure (if partner 1 chewed A and partner 2 chewed B)
3. Explain how the data you collected can be both qualitative and quantitative;
Two ways I could explain my results after stretching each piece of gum would be; B was stretchier and longer than A (qualitative), or B was longer than A by about 270cm (quantitative).
4. Were SI units used in this lab?
5. Yes, we used centimetres to measure the length/diameter of the gum throughout the lab.
1. We started with creating a number of pentagons and tried to connect them all, but it was difficult as they kept falling apart and it was hard to tell which parts to connect to what. After that, we took everything apart and decided on creating a smaller version of our ball, but with hexagons (rather than pentagons), and though it was sturdier, it was still difficult to connect everything, as well as make a circle. We later gave up and ended with an object that stood up, but wasn’t nearly a soccer ball.
2. We learned that it was much more difficult than we expected. When the shape is bigger, it is harder to get to stand up and create what we want, but when smaller, it stands up, but still doesn’t look like a soccer ball.
3. This is a math problem because it takes a certain amount hexagons and pentagons to create a round soccer ball. The creators of the soccer ball used geometry (squares and circles) to make it and others continue to create new versions using the same math techniques.
