A house painter has found that the number of job 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) = 104.35 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. D 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 your calculator before reporting the answer with all numerical values rounded to three decimal places.) p(x) = dollars per job✔✔✔ gives the average amount the painter was paid per job x years since 2004✓✓✔ 0≤x≤6 (b) The equation for the painter's annual income is t(x) = (x)p(x)✔✔✔ 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. $ Do not round intermediate steps. Round your final answer as instructed. 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 job 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) = 104.35 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. D 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 your calculator before reporting the answer with all numerical values rounded to three decimal places.) p(x) = dollars per job✔✔✔ gives the average amount the painter was paid per job x years since 2004✓✓✔ 0≤x≤6 (b) The equation for the painter's annual income is t(x) = (x)p(x)✔✔✔ 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. $ Do not round intermediate steps. Round your final answer as instructed. 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
Related questions
Question
Transcribed Image Text:A house painter has found that the number of job 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
104.35 jobs
j(x) =
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 your calculator
before reporting the answer with all numerical values rounded to three decimal places.)
p(x) =
dollars per job
gives the average amount the painter was paid per job x years since 2004✓ ✔
. 0≤x≤6
(b) The equation for the painter's annual income is t(x) = [j(x)p(x)
✔ 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.
$
Do not round intermediate steps. Round your final answer as instructed.
Using the unrounded models above, how rapidly was the painter's income changing in 2010? (Round your answer to two decimal places.)
$
per year
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
