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# Mathematics - Linear Operators

Please see the attached file for the fully formatted problems.

A defense attorney charges her client
\$4000 plus \$120 per hour. The formula R _ 120n _ 4000
gives her revenue in dollars for n hours of work. What is
her revenue for 100 hours of work? What is her revenue
for 101 hours of work? By how much did the one extra
hour of work increase the revenue? (The increase in
revenue is called the marginal revenue for the 101st hour.)

96. Single women. The percentage of women in the 20-24 age
group who have never married went from 55% in 1970 to
73% in 2000 (Census Bureau, www.census.gov). Let 1970
be year 0 and 2000 be year 30.
a) Find and interpret the slope of the line through the
points (0, 55) and (30, 73).
b) Find the equation of the line in part (a).
c) What is the meaning of the y-intercept?
d) Use the equation to predict the percentage in 2010.
e) If this trend continues, then in what year will the
percentage of women in the 20-24 age group who have
never married reach 100%?

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