Assignment 12

Investigating the Increase in First Class Letter Postage

Over the Last Eighty Years

by Patricia Johnson

Below is a table showing the first class postage rates for the US Mail from 1919 to 1999.

 year rate(in cents) 1919 2 1932 3 1958 4 1963 5 1968 6 1971 8 1974 10 1975 13 1978 15 1981 20 1985 22 1988 25 1991 29 1994 32 1999 33

A graph of this data is shown below.

The above graph seems to predict exponential growth of the cost of first class postage over the past eighty years. By using a graphing calculator the following exponential function was obtained as a best representation of the data.

where y = postage rate in cents

x = number of years

a = 1.385016973

b = 1.039947669

We will use this function to generate a new set of data. This data will then be used to plot the graph of the function. This data can then be used to predict:

a) when the cost of a first class postage stamp will reach 64 cents and \$1.00.

b) how soon to expect the next 3 cents increase.

 Year No. of years Rate (in cents) 1919 0 1.385016973 1932 13 2.3046469817656 1958 39 6.38121007015968 1963 44 7.7617646650452 1968 49 9.44099787550744 1971 52 10.6182355992007 1974 55 11.9422680448462 1975 56 12.419333815811 1978 59 13.967952771551 1981 62 15.7096755366937 1985 66 18.3743996641933 1988 69 20.6655808211155 1991 72 23.242458990717 1994 75 26.1406589348405 1999 80 31.7961077304521 2000 81 33.0662881175565 2001 82 34.3872092503353 2002 83 35.7608981033015 2015 96 59.5055854806489 2016 97 61.882694913081 2017 98 64.3547643262968 2018 99 66.9255871501767 2025 106 88.0384911211008 2026 107 91.555423623666 2027 108 95.212849381739 2028 109 99.0163807733876 2029 110 102.971854378101 2030 111 107.085339933113

From the graph it appears that:

a) the cost of a first class postage stamp will reach 64 cents in about the year 2017 and \$1.00 about the year 2028.

b) the next 3 cents increase will occur in the year 2002.

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