Question
A house painter has found that the number of jobs that he has each year is decreasing with respect to the number of years he has been in business. The number of jobs he has each year can be modeled
j(x) = 104.55 jobs
X
where x is the number of years since 2004. The painter has kept records of the average amount he was paid for each job. His income per job is presented in the table.
Average Income per Job
Income (dollars)
Year
2004
430
2005
559
2006
727
2007
945
2008
1228
2009
1597
2010
2075
(a) Find an exponential model for average income per job, p, with input x aligned to years since 2004. (Remember to paste the unrounded function model into your calculator before reporting the
answer with all numerical values rounded to three decimal places.)
p(x) 430.07(1.300)*
dollars per job gives the average amount the painter was paid per job x years after 2004, 0 s x s 6
(b) The equation for the painter's annual income is tx) = j(x)p(x)
dollars.
(c) What was the painter's income in 2010? (Remember to avoid intermediate rounding.) Round your answer to two decimal places.
36171.96
How rapidly was the painter's income changing in 2010? (Round your answer to two decimal places.)
$237.73
Xper year
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Transcribed Image Text:A house painter has found that the number of jobs that he has each year is decreasing with respect to the number of years he has been in business. The number of jobs he has each year can be modeled j(x) = 104.55 jobs X where x is the number of years since 2004. The painter has kept records of the average amount he was paid for each job. His income per job is presented in the table. Average Income per Job Income (dollars) Year 2004 430 2005 559 2006 727 2007 945 2008 1228 2009 1597 2010 2075 (a) Find an exponential model for average income per job, p, with input x aligned to years since 2004. (Remember to paste the unrounded function model into your calculator before reporting the answer with all numerical values rounded to three decimal places.) p(x) 430.07(1.300)* dollars per job gives the average amount the painter was paid per job x years after 2004, 0 s x s 6 (b) The equation for the painter's annual income is tx) = j(x)p(x) dollars. (c) What was the painter's income in 2010? (Remember to avoid intermediate rounding.) Round your answer to two decimal places. 36171.96 How rapidly was the painter's income changing in 2010? (Round your answer to two decimal places.) $237.73 Xper year
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