Monday, April 21, 2014

Polar Graphs

In Pre-Calculus, we've been learning about polar graphs using Desmos. We were told to use the program to create an intricate flower like design using new equations we had learned about. 
To start, I used a simple r=asin(b*theta) equation, making "a" and "b" sliders, to create a basic four petaled flower. 




Next, I played around with the values to create the picture below. I found that the "a" value made the graph bigger or smaller while the "b" value changed the number of "petals".


After learning some of the basics, I began to get creative and used multiple equations and sliders, including r=asin(b*theta) and r=acos(b*theta) and the Spiral of Archimedes (r=theta), to make an intricate flower pattern. While I chose not to use it, we also learned about Limacon graphs: r=a+bsin(theta) and r=a+bcos(theta). By only changing the "a" and "b" values slightly, I was able to drastically change the graph's pattern. So even though only a few equations were used, many different patterns were able to be made.


After the graph was actually produced, I changed the aesthetic appearance of the graph to yield the final product.








Sunday, December 8, 2013

Loan Project

When it comes to college loans, there are a few different options to choose from. You may apply for a bank loan, a government subsidized loan, or a government unsubsidized loan. A bank loan, obviously is taken out through your bank. Sallie Mae, for example, offers interest rates for student loans between 3.17% and 9.37%. A government subsidized loan is a loan option offered by the government for lower income families and offers a 3.86% interest rate. Finally, a government unsubsidized loan is a loan option offered by the government to any student. It's undergraduate interest rate is 3.86% however, it jumps to 5.41% for graduate students.
If we take out a $5,000 loan every year for fours years, we can use the equation A=P(1+r)^t to figure out how long it will take to pay of the loans where A is the amount owed with interest, P is the principle amount borrowed, r is the interest rate divided by 100, and t is the amount of time in years.
Say we take out four government unsubsidized loans,one for each year of college. To calculate how much money has to be repaid on the Freshman year loan at the end of our four years in college, we use set up the equation as follows: A=5000(1+.0386)^4. The 4 represents the four years that it will be accumulating interest. When we use that same equation for four years, only changing the value of t, we will have four totals. For the freshman loan, $5,817.86. For sophomore year, $5,601.64. For junior year, $5393.45. For senior year, $5193.00. This gives a total debt of $22,005.95.
Now, since that total will continue to accumulate interest as it is paid off, we can't simply divide it by a certain number of year to find the monthly payments. Instead, we us the equation from earlier. This time, it is A=22005.95(1+.0386)^15. In this case, we are going to determine how much money will have to be paid each year to pay off the debt in fifteen years. In fifteen years, it the debt new amount owed will be $38,838.72. To find the monthly bill, we divide $38,838.72 by 15 times twelve: 38838.72/(15*12). We multiply fifteen by twelve to get the monthly bill since there are twelve months in a year. Therefore, it will cost $215.76 per month for fifteen years to pay off the student debt.

Thursday, September 19, 2013

Geogebra #1


After I got the hang of it, this assignment made a lot more sense. My Geogebra used a lot of mirror images by making a function negative like "y=x^2" and "y=-x^2". I also used sin functions to make the "wavy" lines in the middle ("y=sin(x+3)" and "y=-sin(x+3)"). By putting a number over "x", I was able to make the outside curving lines that stay in their given quadrant (ex: -3/x). My total functions were as follows: