Question

a company training program has determined that, on the average, a new employee produces ( p(s) ) items per day after ( s ) days of on - the - job training, where ( p(s)=\frac{68 s}{s + 5} ). find and interpret ( lim _{s
ightarrow infty} p(s) ).
find the limit. select the correct choice below and, if necessary, fill in the answer box within your choice.
a. ( lim _{s
ightarrow infty} p(s)=68 )
b. the limit does not exist and is not ( infty ) or ( -infty ).
interpret the limit. select the correct choice below and fill in the answer box within your choice.
a. the number of days of training for a new employee gets closer and closer to ( square ) as the number of items that employee produces increases.
b. the number of days of training for a new employee gets closer and closer to ( square ) as the number of items that employee produces decreases.
c. the number of items a new employee produces gets closer and closer to ( square ) as the number of days of training decreases.
d. the number of items a new employee produces gets closer and closer to ( square ) as the number of days of training increases.

Explanation:

Step1: Divide numerator and denominator by \(s\)

Given \(P(s)=\frac{68s}{s + 5}\). Divide numerator and denominator by \(s\):

$$
LATEXBLOCK0
$$

Step2: Evaluate the limit

We know that \(\lim_{s
ightarrow\infty}\frac{1}{s}=0\). So, \(\lim_{s
ightarrow\infty}\frac{5}{s}=0\). Then:

$$ \lim_{s ightarrow\infty}\frac{68}{1+\frac{5}{s}}=\frac{68}{1 + 0}=68 $$

For the interpretation, the limit \(\lim_{s
ightarrow\infty}P(s)\) means as \(s\) (the number of days of training) increases, \(P(s)\) (the number of items produced) approaches the limit value.

Answer:

A. \(\lim_{s
ightarrow\infty}P(s)=68\)

D. The number of items a new employee produces gets closer and closer to \(68\) as the number of days of training increases.