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The daily output of a worker who has been on the job for t weeks is given by a function of the form tex2html_wrap_inline39 . 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 tex2html_wrap_inline53 . Use Q(1)=30 to find tex2html_wrap_inline57 :


    Now we know that tex2html_wrap_inline59 . 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, tex2html_wrap_inline69 approaches 0, so tex2html_wrap_inline59 approaches 40-20(0)=40 units a day.

Carl Lee
Fri Nov 6 09:35:16 EST 1998