Section+1.1


 * Section 1.1**


 * Modeling and Equation Solving (pg. 71-85)**
 * Homework for this Section: Pg. 81: (1-10)**

Three Types of Mathematical Modeling: **Numerical, Algebraic, Graphical**

> - **Data is analyzed** > - **Table** > - **Excel** > > > **Example (pg. 70)**: The numbers in the table show the growth of the minimum hourly wage (MHW) from 1955 to 2005. > b.) In what year did a worker eaing the MHW enjoy the greatest purchasing > c.) A worker on minimum wage in 1980 was earning nearly twice as much as > > **Solution:** > a.) In the period 1975 to 1980 it increased by $1.00. Notice that the minimum wage > b.) 1970 > c.) Although the MHW increased from $1.60 to $3.10 in that period, the purchasing power > actually dropped by $0.57 (in 1996 dollars). This is one way inflation can affect the economy. 
 * 1.) Numerical Modeling (pg. 70) : the most basic kind of mathematical model. Numbers are analyzed to gain insights into phenomen Key information from class
 * Year || MHW || Purchasing Power in 1996 Dollars ||
 * 1955 || 0.75 || 4.39 ||
 * 1960 || 1.00 || 5.30 ||
 * 1965 || 1.25 || 6.23 ||
 * 1970 || 1.60 || 6.47 ||
 * 1975 || 2.10 || 6.12 ||
 * 1980 || 3.10 || 5.90 ||
 * 1985 || 3.35 || 4.88 ||
 * 1990 || 3.80 || 4.56 ||
 * 1995 || 4.25 || 4.38 ||
 * 2000 || 5.15 || 4.69 ||
 * 2005 || 5.15 || 4.15 ||
 * a.) In what 5-year period did the actual MHW increase the most?
 * a.) In what 5-year period did the actual MHW increase the most?

 > Key information from class > - **uses formulas to relate variable quantities** > > **Example (pg. 71)**: There are two pizzas, one large normal pizza with a diameter of 23" and the other Sicilian style pizza which is > 18" by 24". Which pizza is the better deal if they both have the same cost? First Find the Area of Both Pizzas: A = L x W > //Area of Sicilian Style Pizza: A = 18(24) > = 432 in^2 > Area of Regular Pizza: A = Pie (11.5)^2 > = 415 in ^2// > **Solution**: Therefore the normal large pizza is the better deal becasue it has a greater area, meaning more pizza for the money.
 * 2.) Algebraic Modeling (pg. 71) : uses formulas to relate variable quantities associated with the phenomena being studied. The added power of an algebraic model over a numerical model is that it can be used to **generate numerical valuse of unknown quantities by relaitng them to known quantities.**

> Key information from class > - **a visible representaion of a mumerical or algebraic model** > > **Example (pg. 73)**: Galilo Galilei rolled balls down inclined planes carefully recording the distance they traveled as a function > of elapsed time. He recorded the data below. What graphical model fits the data? Can you find an algebraic model > that fits?
 * 3.) Graphical Modeling (pg 72) : a visible representation of a numerical model or an algebraic model that gives insight into the relationships between variable quantities. Learning to interpret and use graphs is a major goal of this section.
 * Elapsed Time (sec) || 0 || 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 ||
 * Distance Traveled (in) || 0 || 0.75 || 3 || 6.75 || 12 || 18.75 || 27 || 36.75 || 48 ||


 * Plug this data into your graphing calculator to find solution
 * Solution**: A scatter plot of the data is shown in figure 1.1 on pg. 73. showing [-1, 18] by [-8, 56]


 * Key Terms From Section 1.1:**
 * **Mathematical Model**- a mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior.
 * **Numerical Model**- the most basic kind of mathematical model where numbers (or data) are analyzed to gain insights into phenomena.
 * **Algebraic Model-** uses formulas to relate variable quantities associated with the phenomena being studied. The added power of an algebraic model over a numerical model is that it can be used to generate numerical values of unknown quantities by relating them to known quantites.
 * **Graphical Model-** a visible representation of a numerical model or an algebraic model that gives insight into the relationships between variabl quantities.