Question

Production Rate Suppose the number of items a new worker on an assembly line produces daily after t days on the job is given by

l(t)=45 ln(t+1)
Find the average number of items produced daily by this employee after the following numbers of days.
a. 5
b. 9
c. 30

Answer 1

(a) 81 items

(b) 104 items

(c) 155 items

Explanation:

Given:

The expression for the number of items produced by a new employee daily after 't' days on the job is given as:

`l(t)=45\ln(t+1)`

(a) Number of days (t) = 5

Average number of items produced can be obtained by plugging in 5 for 't' in the above expression. This gives,

`l(t=5)=45\ln(5+1)\\\\l(t=5)=45\ln 6\\\\l(t=5)=80.6\approx 81`

Therefore, nearly 81 items are produced after 5 days.

(b) Number of days (t) = 9

Average number of items produced can be obtained by plugging in 9 for 't' in the above expression. This gives,

`l(t=9)=45\ln(9+1)\\\\l(t=9)=45\ln 10\\\\l(t=9)= 103.6\approx 104`

Therefore, nearly 104 items are produced after 9 days.

(c) Number of days (t) = 30

Average number of items produced can be obtained by plugging in 30 for 't' in the above expression. This gives,

`l(t=30)=45\ln(30+1)\\\\l(t=30)=45\ln 31\\\\l(t=31)=154.5\approx 155`

Therefore, nearly 155 items are produced after 30 days.