Da Vinci

For our Advanced Math class we took a field trip to the science center to explore the Da Vinci exhibit. Those of you who don't know him, Da Vinci was one fo the greatest geniuses the world has ever known. He invented flying machines, robots, and ideal city models. He was a very advanced and ingenus man.

When we first arrived there we examined his "Vitruvian Man". This painting is an example of the golden ration. His arm spam was the same of his height. Each item of his body was proportionate of another part.

Other inventions that we got to see was "Meccanism d' Orologio" which was a clock without batteries, "Ornitotteio Verticale" Vertical flying machine, and "Ponte Salcatico" emergency bridge.  This is his bridge --->


Another of his paintings that we observed was the "Mona Lisa"

Financing

The other day in Advanced Math we learned about financing and interests rates. I learned that if you buy something that costs a lot of money, you could end up spending almost half of what it costs (if you had used a credit card) because of interests rates. I will definitely be careful when I get my card. 

Earthquakes

Haiti: 7.0
Chile: 8.8

Chile's earthquake was 63 times stronger then the earthquake was in Haiti.


The Chilean earthquake moved the land roughly about 8 feet above the shore line.

The reason why we heard more about Haiti's earthquake and not Chile's is in the difference of the country's. Chile was prepared for earthquakes because they have a high risk of them. They have strict building codes to prevent major damage. Haiti didn't have any of this. Haiti is a poor country and had poor construction so there was more damage and lives lost. Also the epicenter of the Chilean earthquake was about 70 miles away from the city while the epicenter of Haiti's earthquake was 10 miles from the city.

Scatter Plot and Linear Regression

 Years                         Population in Billions
0   (1950)                   2.6
1   (1960)                   3
2   (1970)                   3.7
3    (1980)                  4.5
4   (1990)                   5.2
5   (2000)                   6.1
6   (2010)                   6.9
7   (2020)                   7.6
8    (2030)                  8.2
9    (2040)                  8.9
10   (2050)                 9.2

The correlation coefficient is 0.997
The regression equation is y=0.709x+2.445
The slope represents the rate in which the world population grows every ten years and the y-intercept represents  if x were to be 0, that would be the population.

What my data shows is there is a steady growth in the world's population. Also that the numbers such as the y-intercept and first x-y value don't align perfectly because there is not exact information.  

It is important to analyze regression equations and scatter plots to interpret data that has been given to us. They can help with such things as stats on your favorite baseball player to analyzing how much money a stock has made or lost. 

Putting the Function into Functional

Exponential Function:
A population of a city is P = 250342e0.012t where t represent the population in the year 2000.
Find the total population of the city in the year 2010. 
       To find the population in the year 2010 you have to let t = 10 giving you the equation

         P = 250342e0.012(10) which equals 282259.82

 Now this graph on the left is not  the real graph to this equation but this is what it would look like. The numbers on the y-axis would have a much greater value because of the high population growth while the numbers on the x-axis would stay about the same because you are counting by years. Also the angle of elevation would be much great creating a sharper curve.

http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_ExponentsApps.xml




Linear Equation:
A company purchases a computer for $10000. Use a linear graph to show the depreciation of the computer over a 5 year period if each year the computer the depreciates $2000 a year.
     The equation for this problem can be modeled by Y = -2000x+10000.

On the right is the graph of this equation. You put the number of years in the x value in the equation. You can see that after one year the value of the computer is $8000 and after two years the value of the computer is at $6000.


http://hubpages.com/hub/APPLICATIONS--OF-LINEAR-EQUATIONS









Quadratic Equations:
A producer of personal computer mouse covers determines that the number (N) of covers sold is related to the price (x) of a cover by N =  35x-x^2. At what price should the producer price a mouse cover in order to sell 216 of these items.

       What you would do is sub in 216 for N. 216 = 35x-x^2. Move the 216 to the right side of the equation and then solve. You should have answers of x = 8 and x = 27. You will put those back in the equation for x and solve again. In this case both of these x values are correct so you will be order to price them at $8 or $27 to sell 216.

This example doesn't have a graph for an example but generally all x^2 graphs will have a U-shape to them.

http://cnx.org/content/m21915/latest/