1. 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 4.1 1 Age10161542585 Number of pets 412611032

2. Section 4.1 Exponential Modeling AP Statistics

3. AP Statistics, Section 4.1 3 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.

4. AP Statistics, Section 4.1 4 XYDifference 0510-5=5 11015-10=5 21520-15=5 32025-20=5 42530-25=5 53035-30=5 63540-35=5 740 Linear Growth

5. 5 XYDifference 0510-5=5 11025-10=15 42540-25=15 74055-40=15 105575-55=20 147595-75=20 1895115-95=20 22115 Linear Growth 3 3 3 4 4 4 *Thus the original date is approximately linear. Each chunk has the same difference

6. AP Statistics, Section 4.1 6 Exponential Growth is interesting, but what we really want is a linear model

7. AP Statistics, Section 4.1 7 XYDifference 012-1=1 124-2=2 248-4=4 3816-8=8 41632-16=16 53264-32=32 664128-64=64 7128 Exponential Growth

8. AP Statistics, Section 4.1 8 XYRatio 012/1=2 124/2=2 248/4=2 3816/8=2 41632/16=2 53264/32=2 664128/64=2 7128 Exponential Growth

9. AP Statistics, Section 4.1 9 XYRatio 012/1=2 128/2=4 3832/8=4 532128/32=4 7128512/128=4 95124096/512=8 12409632768/4096=8 1532768 Exponential Growth Same ratio for x values with the same gap

10. 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 4.1 10

11. AP Statistics, Section 4.1 11 YearSubscribersRatiosLog(Sub) 1990 5,2833.722880611 1993 16,0094.204364205 1994 24,1341.5075274.382629308 1995 33,7861.3999344.528736778 1996 44,0431.3035874.643876893 1997 55,3121.2558644.742819362 1998 69,2091.2512474.840162574 1999 86,0471.2432924.934735733

12. AP Statistics, Section 4.1 12

13. AP Statistics, Section 4.1 13 YearSubscribersRatiosLog(Sub) 1990 5,2833.722880611 1993 16,0094.204364205 1994 24,1341.5075274.382629308 1995 33,7861.3999344.528736778 1996 44,0431.3035874.643876893 1997 55,3121.2558644.742819362 1998 69,2091.2512474.840162574 1999 86,0471.2432924.934735733 Means 50.7% growth in subscribers that year. Log will undo exponentiation

14. AP Statistics, Section 4.1 14

15. AP Statistics, Section 4.1 15

16. AlgebraicProperties ofLogarithms. AP Statistics, Section 4.1 16

17. 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

18. AP Statistics, Section 4.1 18 Assignment Exercises: 4.6, 4.8, 4.9, 4.11, 4.19, 4.21