Chapter 4.1, Problem 73E

Postal Rates U.S postal rates have steadily increased since 1932. Using data depicted in the table for the years 1932-2013, the cost in cents to mail a single letter can be modelled using a quadratic formula as follows:

$C\left(t\right)=0.007756t^2-0.04258t+0.7585$ where t is the number of years since 1932. Source: U.S. Postal Service.

Year	Cost	Year	Cost
1932	3	1988	25
1958	4	1991	29
1963	6	1995	32
1971	8	2001	34
1974	10	2002	37
1975	13	2006	39
1978	15	2007	41
1981	18	2008	42
1981	20	2009	44
1985	22	2012	45
		2013	46

a. Find the predicted cost of mailing a letter in $1982$ and $2002$ and compare these estimates with the actual rates.

b. Find the rate of change of the postage cost for the years $1982$ and $2002$ and interpret your results.

c. Using the regression feature on a graphing calculator, find a cubic function that models these data, letting $t=0$ correspond to the year $1932.$ Then use your answer to find the rate of change of the postage cost for the years $1982$ and $2002$.

d. Discuss whether the quadratic or cubic function best describes the data. Do the answers from part b or from part c best describe the rate that postages was going up in the years $1982$ and $2002$?

e. Explore other functions that could be used to model the data, using the various regression features on a graphing calculator, and discuss to what extent any of them are useful descriptions of the data.

f.

g.