4.1 Warm Up Describe a monotonic function. Enter the given data in L1 and L2 Create a scatter plot for the data. Determine if a linear model is a good.

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4.1 Warm Up Describe a monotonic function. Enter the given data in L1 and L2 Create a scatter plot for the data. Determine if a linear model is a good model. If so what is the equation for the LSRL, If not what would you do to transform the data. AP Statistics, Section Age Number of pets

Section 4.1 Exponential Modeling AP Statistics

AP Statistics, Section Growth and Decay Linear growth increases by a fixed amount in each equal time period Exponential growth increase by a fixed percentage of the previous total.

AP Statistics, Section XYDifference = = = = = = =5 740 Linear Growth

5 XYDifference = = = = = = = Linear Growth *Thus the original date is approximately linear. Each chunk has the same difference

AP Statistics, Section Exponential Growth is interesting, but what we really want is a linear model

AP Statistics, Section XYDifference 012-1= = = = = = = Exponential Growth

AP Statistics, Section XYRatio 012/1=2 124/2=2 248/4=2 3816/8= /16= /32= /64= Exponential Growth

AP Statistics, Section XYRatio 012/1=2 128/2=4 3832/8= /32= /128= /512= /4096= Exponential Growth Same ratio for x values with the same gap

Exponential? To check if a curve is truly exponential you need to look at the ratio between a value and the previous output. Skip non-consecutive values. AP Statistics, Section

AP Statistics, Section YearSubscribersRatiosLog(Sub) , , , , , , , ,

AP Statistics, Section

AP Statistics, Section YearSubscribersRatiosLog(Sub) , , , , , , , , Means 50.7% growth in subscribers that year. Log will undo exponentiation

AP Statistics, Section

AP Statistics, Section

AlgebraicProperties ofLogarithms. AP Statistics, Section

Example Enter in list 1  0,1,2,3,4,5 Enter in list 2  1,2,4,8,16,32 Enter in list 3  Log(L2) See results  Graph L1 and L2 Calculate r for L1 and L2  Graph L1 and L3 Calculate r for L1 and L3 17

AP Statistics, Section Assignment Exercises: 4.6, 4.8, 4.9, 4.11, 4.19, 4.21