   Chapter 4.6, Problem 44E ### 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 in Exercise 43 requires that a new employee be producing at least 20 units per day after 30 days on the job.(a) Find a learning curve model that describes this minimum requirement.(b) Find the number of days before a minimal achiever is producing 25 units per day. How does this compare to the number of days found using the model from Exercise 43?

(a)

To determine

To calculate: The learning curve model that describes the requirement that a new employee will be producing at least 20 units per day after 30 days on the job.

Explanation

Given Information:

The provided information is that a new employee will be producing at least 20 units per day after 30 days on the job.

Formula used:

The number of units N produced par day after a new employee has worked for t days is modeled by the equation:

N=30(1ekt)

Calculation:

Consider the provided information that a new employee will be producing at least 20 units per day after 30 days on the job.

Observe that at t=30, N=20

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

20=30(1ek×30)20=30(1e30k)1e30k=2030e30k=12030

Solve further,

e

(b)

To determine

To calculate: The number of days before a minimal achiever is producing 25 units per day using the learning curve model that describes the requirement that a new employee will be producing at least 20 units per day after 30 days on the job as calculated in part (a).

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