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.