1. Minimum Average Cost: The average cost per hour in dollars, C‾, of producing x riding lawn mowers can be modeled by the function
C‾(x) = 0.3x2 + 21x - 251 + 2500/x
(a) Use a graphing utility to graph C‾ = C‾(x).
(b) Determine the number of riding lawn mowers to produce in order to minimize average cost.
(c) What is the minimum average cost?
2. e-Filing Tax Returns: The Internal Revenue Service Restructuring and Reform Act (RRA) was signed into law by President Bill Clinton in 1998. A major objective of the RRA was to promote electronic filing of tax returns. The data in the table that follows show the percentage of individual income tax returns filed electronically for filing years 2000-2008. Since the percentage P of returns filed electronically depends on the filing year y and each input corresponds to exactly one output, the percentage of returns filed electronically is a function of the filing year; so P(y) represents the percentage of returns filed electronically for filing year y.
|
Year
|
Percentage of returns e-filed
|
|
2000
|
27.9
|
|
2001
|
31.1
|
|
2002
|
35.9
|
|
2003
|
40.6
|
|
2004
|
47.0
|
|
2005
|
51.8
|
|
2006
|
54.5
|
|
2007
|
58.0
|
|
2008
|
59.8
|
(a) Find the average rate of change of the percentage of e-filed returns from 2000 to 2002.
(b) Find the average rate of change of the percentage of e-filed returns from 2004 to 2006.
(c) Find the average rate of change of the percentage of e-filed returns from 2006 to 2008.
(d) What is happening to the average rate of change as time passes?