14. Suppose a manufacturer opens a new plant to produce an advanced piece of medical equipment. At first, the workers are untrained, and the process is being tweaked, but they expect after a few weeks they will be producing at a rate of 400 pieces of medical equipment per week. The model they are using to predict this is dm = 400 1- 425 dt where i is time since the plant opened, in weeks, and (5 +1)" m is the total number of pieces of medical equipment they have produced since opening (m (0) = 0). a. Evaluate - dt " at f =1 and round to the nearest whole number. Interpret this value in the context of the problem. b. How many weeks will it take for the plant to increase their production level to 300 pieces of medical equipment per week? c. Determine how many pieces of medical equipment the plant will produce from the day it opened to the end of the 6th week. d. What is the average production rate for the first 6 weeks