Psychology—Memory Studies: The technicians at the Arp Brothers auto parts factory are give...

Psychology—Memory Studies: The technicians at the Arp Brothers auto parts factory are given a checklist of 40 items to inspect for quality control. Over the next three months, a technician is selected and asked to write the checklist from memory. The mathematical model for the technician’s performance is given by

where x represents the number of days since the checklist was distributed and f(x) represents the average number of inspection items that was remembered.

(a) Evaluate f(2) and f(30) and interpret each.

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(b) Find the horizontal asymptote and interpret its meaning.

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(c) The State Regulatory Agency requires technicians to remember a minimum of 25 items after three months. According to the model, will the technicians meet this requirement?