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.

       

a. Find a logistic model for the data in the accompanying table.
b. Write the derivative equation for the model.
c. On the interval from week 1 through week 19, when is the cumulative number of labor hours increasing most rapidly? How many labor hours are needed in that week?  
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?

Cumulative Labor-Hours by the Number of Weeks after Job Begins Weeks 1 4 7 10 13 16 19 Hours 25 158 1254 5633 9280 10,010 10,100