Which graph best describes your excitement for …..

We are going to analyze graphs and tables to make an informed decision as to which function would best model a given set of data.

Decision Making Exponential Quadratic The three most common are…. When given a data set and asked to find a model, it helps to first know what model is best. The three most common are…. Linear Exponential Quadratic

Linear Models Linear Models have a common ratio. When looking at a table, the change in y over the change in x should be the same. x y -3 7 -1 13 1 19 3 25 5 31 +6 +2 +6 +2 +2 +6 +2 +6

Exponential Models x y -2 -1 -8 -32 1 -128 2 -512 Exponential models have a common ratio. When looking at a table, the y values should appear to be multiplied by the same value. x y -2 -1 -8 -32 1 -128 2 -512 X 4 +1 X 4 +1 +1 X 4 +1 X 4

Quadratic Models For quadratic data, the second differences are the same. If data have a common second difference, then you can model them with a quadratic function. x y -1 16 2 1 -2 4 3 20 +1 -14 -10 +1 -4 -10 +1 +6 -10 +1 +16

Graphing Calculator It is often easiest to determine the best model by the shape of the graph. Then find the regression. To do this: 1. Turn the scatter plot on using 2. Enter the data into 1: Edit Press 9: Stat. Analyze the shape of the graph. Use CALC and choose LinReg, QuadREg or ExpReg. 2nd Y = STAT ZOOM STAT

Let’s Try Some!!!! x y -1 20 8 1 3.2 2 1.28 3 0.512

x y 1 1.5 2 6 3 13.5 4 24

The table below shows the population of a small town The table below shows the population of a small town. Let t = 0 correspond to the year 1990. a. Graph the data. Does the graph suggest a linear, exponential, or quadratic model? b. What is the difference in years? c. Find the differences of consecutive terms. Divide by the difference in years to find possible common differences. d. Write a linear equation to model the data based on your answer to part (c). e. Predict the population in 2020. Year y 5100 5 5700 10 6300 15 6900 20 7500