   Chapter 4.6, Problem 43E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Learning Curve The management of a factory finds that the maximum number of units a worker can produce in a day is 30. The learning curve for the number of units N produced per day after a new employee has worked for t days is modeled by N   = 30 ( 1   − e k t ) . After 20 days on the job, a worker is producing 19 units in a day. How many more days should pass before this worker is producing 25 units per day?

To determine

To calculate: The number of days after which the worker will be producing 25 units per day if after 20 days the workers are producing 19 units in a day and the number of units N produced par day after a new employee has worked for t days is modeled by N=30(1ekt).

Explanation

Given Information:

The provided information is that after 20 days the workers are producing 19 units in a day and the number of units N produced par day after a new employee has worked for t days is modeled by N=30(1ekt).

Calculation:

Consider the provided information that after 20 days the workers are producing 19 units in a day and the number of units N produced par day after a new employee has worked for t days is modeled by N=30(1ekt).

Observe that at t=20, N=19.

Substitute t=20 and N=19 in the equation N=30(1ekt),

19=30(1ek×20)19=30(1e20k)1e20k=1930e20k=11930

Solve further,

e20k=1130

Take natural log on both the sides as,

ln e20k=ln(1130)20kln e=ln(1130)k=ln(1130)20

Hence, the value of k is ln(1130)20 which is approximately 0

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