Need help with c and d \
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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Need help with c and d
\
Transcribed Image Text:The personnel manager for a construction company keeps track of the total number of labor hours spent on a construction job each week during the construction. Some of the
weeks and the corresponding labor hours are given in the table.
Cumulative Labor-Hours by the Number of
Weeks after Job Begins
Weeks (x)
1
f(x) =
4
7
10
13
16
19
Hours (f)
10108.729
1+1158.494e-0.728x
26
159
1251
5632
9278
10,007
(a) Find the function for the logistic model that gives total number of labor hours where x is the number of weeks after construction begins, with data from 1 ≤ x ≤ 19.
(Round all numerical values to three decimal places.)
10,099
(b) Write the derivative equation for the model. (Round all numerical values to three decimal places.)
f'(x) = 8525536.579(e-0.728x) (1+1158.494e-0.728x)-2
(c) On the interval from week 1 through week 19, when is the cumulative number of labor hours increasing most rapidly? (Round your answer to three decimal places.)
weeks
How many labor hours are needed in that week? (Round your answer to three decimal places.)
labor hours
(d) If the company has a second job requiring the same amount of time and the same number of labor hours, a good manager will schedule the second job to begin when
the number of cumulative labor hours per week for the first job begins to increase less rapidly. How many weeks into the first job should the second job begin?
weeks
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