he 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) Hours (f) 1 27 4 157 7 1257 10 5631 13 9279 16 10,013 19 10,101
he 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) Hours (f) 1 27 4 157 7 1257 10 5631 13 9279 16 10,013 19 10,101
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 2TI: Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time...
Related questions
Question
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 after Job Begins
Weeks (x) | Hours (f) |
---|---|
1 | 27 |
4 | 157 |
7 | 1257 |
10 | 5631 |
13 | 9279 |
16 | 10,013 |
19 | 10,101 |
(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.)
f(x) =
(b) Write the derivative equation for the model. (Round all numerical values to three decimal places.)
f '(x) =
(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
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 4 steps with 1 images
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
Not clear on answers for b and second part of c
Solution
by Bartleby Expert
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning