help with 5-9

MacBook Pro Chapter 5 Protest Exmanentinand Loerithmic Functions Name w The United States Postal system has been basing the price of a first-class stamp on a full ounce since July 1, 1885. Below is a table that gives the price of a first-class stamp by year since 1885 1. Complete the middle column of the table. Year Let the number of years Price of a class stamp since 1885 s COD 90 Data for LE Data for La 1885 0 02 1917 32 03 1919 39 02 1932 92 03 1958 04 1963 73 05 1968 83 06 1971 08 1974 89 10 1975 13 1978 IS 1981 96 18 1981 96 20 1985 loo 22 1988 103 1991 106 29 1995 le 32 1999 1141 33 2001 16 34 2002 117 37 2006 121 39 2007 122 41 2009 44 129 2. Let x be the number of years since 1885. Use the TI-83 or TI-83 Plus calculator to create a model that is a function of the years past 1885 that will predict the price of a first-class stamp (Press STAT and EDIT on your calculator and enter the data from column 2 above to the L column. Next, enter the data from column 3 to the La column on your calculator. Use the graphing calculator to determine the exponential regression that models these data. Round each number in your model to three decimal places. 0.036 ExpReg: Price P(x) = 0.006. MacBook Pro 1. Use your model to predict the price of a first-dan mamp in 2009 = 0,52164 52 006 dox (1) 0.034 bin 2015 .006 0.36136) - 0.64662043 21.65 4. Use your model to predict the year in which the price of a first-class stamp will be cents (Round to the closest year) 0.50 3.0062 0.36* See 250 doo 6 0.036* = In ) = * = Os In () - 122.65 2123 1885+123 - 2008 price will be 50 cents in 2008 e 5. Use your original function and solve for that is, solve for the logarithmic function that predicts the years past 1885 given the price of a first class stamp (This new function will be the inverse of your original model Instead of having price as a function of years past 1885, you will have the years past 1885 as a function of price.) 2 MacBook Pro 6. Using your model from problem 5 to predict the year in which the first class stamp will be 55 cents . 7. Comment on the accuracy of the models (Underestimation, overestimation) 8. Find a new model that predicts the price of the stamp by using the data starting from 1963 instead of from 1885. Create a scatter plot and create a "best fit" curve to this data 9. Use your new model to predict the price of a stamp in 2009 MacBook Pro Chapter 5 Protest Exmanentinand Loerithmic Functions Name w The United States Postal system has been basing the price of a first-class stamp on a full ounce since July 1, 1885. Below is a table that gives the price of a first-class stamp by year since 1885 1. Complete the middle column of the table. Year Let the number of years Price of a class stamp since 1885 s COD 90 Data for LE Data for La 1885 0 02 1917 32 03 1919 39 02 1932 92 03 1958 04 1963 73 05 1968 83 06 1971 08 1974 89 10 1975 13 1978 IS 1981 96 18 1981 96 20 1985 loo 22 1988 103 1991 106 29 1995 le 32 1999 1141 33 2001 16 34 2002 117 37 2006 121 39 2007 122 41 2009 44 129 2. Let x be the number of years since 1885. Use the TI-83 or TI-83 Plus calculator to create a model that is a function of the years past 1885 that will predict the price of a first-class stamp (Press STAT and EDIT on your calculator and enter the data from column 2 above to the L column. Next, enter the data from column 3 to the La column on your calculator. Use the graphing calculator to determine the exponential regression that models these data. Round each number in your model to three decimal places. 0.036 ExpReg: Price P(x) = 0.006. MacBook Pro 1. Use your model to predict the price of a first-dan mamp in 2009 = 0,52164 52 006 dox (1) 0.034 bin 2015 .006 0.36136) - 0.64662043 21.65 4. Use your model to predict the year in which the price of a first-class stamp will be cents (Round to the closest year) 0.50 3.0062 0.36* See 250 doo 6 0.036* = In ) = * = Os In () - 122.65 2123 1885+123 - 2008 price will be 50 cents in 2008 e 5. Use your original function and solve for that is, solve for the logarithmic function that predicts the years past 1885 given the price of a first class stamp (This new function will be the inverse of your original model Instead of having price as a function of years past 1885, you will have the years past 1885 as a function of price.) 2 MacBook Pro 6. Using your model from problem 5 to predict the year in which the first class stamp will be 55 cents . 7. Comment on the accuracy of the models (Underestimation, overestimation) 8. Find a new model that predicts the price of the stamp by using the data starting from 1963 instead of from 1885. Create a scatter plot and create a "best fit" curve to this data 9. Use your new model to predict the price of a stamp in 2009