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 as j(x) = 104.95 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 Year 2004 2005 2006 2007 2008 2009 2010 Income (dollars) 430 559 727 945 1228 1597 2075 (a) Fill in the blanks to complete 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 you calculator before reporting the answer with all numerical values rounded to three decimal places.) p(x) = ---Select--- ✓gives the average amount the painter was paid per job ---Select--- ✓, 0≤x≤6 (b) The equation for the painter's annual income is t(x) = ---Select--- ✓ dollars. (c) Using the unrounded models above, what was the painter's income in 2010? (Remember to avoid intermediate rounding.) Round your answer to two decimal places. $ Using the unrounded models above, how rapidly was the painter's income changing in 2010? (Round your answer to two decimal places.) $ per year
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 as j(x) = 104.95 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 Year 2004 2005 2006 2007 2008 2009 2010 Income (dollars) 430 559 727 945 1228 1597 2075 (a) Fill in the blanks to complete 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 you calculator before reporting the answer with all numerical values rounded to three decimal places.) p(x) = ---Select--- ✓gives the average amount the painter was paid per job ---Select--- ✓, 0≤x≤6 (b) The equation for the painter's annual income is t(x) = ---Select--- ✓ dollars. (c) Using the unrounded models above, what was the painter's income in 2010? (Remember to avoid intermediate rounding.) Round your answer to two decimal places. $ Using the unrounded models above, how rapidly was the painter's income changing in 2010? (Round your answer to two decimal places.) $ per year
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 as
104.95
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.
j(x)
=
- jobs
Average Income per Job
Year
2004
2005
2006
2007
2008
2009
2010
Income (dollars)
430
---Select---
559
727
945
1228
1597
2075
(a) Fill in the blanks to complete 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 you
calculator before reporting the answer with all numerical values rounded to three decimal places.)
p(x)
✓gives the average amount the painter was paid per job |---Select---
0≤x≤6
(b) The equation for the painter's annual income is t(x)
= ---Select--- dollars.
(c) Using the unrounded models above, what was the painter's income in 2010? (Remember to avoid intermediate rounding.) Round your answer to two decimal places.
Using the unrounded models above, how rapidly was the painter's income changing in 2010? (Round your answer to two decimal places.)
per year
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