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 4 7 10 13 16 19 Hours ( 23 156 1252 5636 9278 10,013 10,099 (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 1sxs 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.) 28- (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) How many labor hours are needed in that week? (Round your answer to three decimal places.) labor hours