QUIZ #8 SOLUTION

The daily output of a worker who has been on the job for t weeks is given by a function of the form . Initially the worker could produce 20 units a day, and after 1 week the worker can produce 30 units a day.

1. How many units will the worker produce per day after 3 weeks?

   First use Q(0)=20 to find A:

   

   Now we know that . Use Q(1)=30 to find :

   

   Now we know that . Find Q(3):

   

2. How many units will the worker produce per day in the long run?

   What value does Q(t) approach as t approaches infinity? As t approaches infinity, approaches 0, so approaches 40-20(0)=40 units a day.

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