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Which graph best describes your excitement for …..

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. When given a data set and asked to find a model, it helps to first know what model is best.

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Which graph best describes your excitement for …..

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  1. Which graph best describes your excitement for …..

  2. 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.

  3. Decision Making 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

  4. 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. +6 +2 +6 +2 +2 +6 +2 +6

  5. Exponential Models Exponential models have a common ratio. When looking at a table, the y values should appear to be multiplied by the same value. X 4 +1 X 4 +1 +1 X 4 +1 X 4

  6. 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. +1 -14 +10 +1 -4 +10 +1 +6 +10 +1 +16

  7. 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, QuadRegor ExpReg. 2nd Y = STAT ZOOM STAT

  8. Let’s Try Some!!!! Looking at the graph, it appears to be either quadratic or exponential. If we find the common ratio, we notice that the common ratio is consistently 0.4. This makes the graph exponential. Using ExpReg, the best-fit equation is

  9. Looking at the graph, it appears to be either quadratic or exponential. If we find the common ratio, we notice it is not the same for all. So we try second differences. The common second difference is 4. This makes the graph quadration. Using QuadReg, the best-fit equation is

  10. 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? The data appears to be linear. b. What is the difference in years? The difference in years is 5. c. Find the differences of consecutive terms. Divide by the difference in years to find possible common differences. The common difference in the y’s is 600. 600/5 = 120. This is the slope. d. Write a linear equation to model the data based on your answer to part (c). The y-intercept (0, 5100), so the equation is y = 120X + 5100. • Predict the population in 2020. In 2020, x = 30. The population will be 8700.

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