   Chapter 12.2, Problem 50E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Productivity Because a new employee must learn an assigned task, production will increase with time. Suppose that for the average new employee, the rate of performance is given by d N d t = 1 2 t + 1 where N is the number of units completed t hours after beginning a new task. If 2 units are completed after 3 hours, how many units are completed after 8 hours?

To determine

To calculate: The number of units completed after 8 hours if 2 units are completed after 3 hours and for the average new employee, the rate of performance is given by dNdt=12t+1.

Explanation

Given Information:

For the average new employee, the rate of performance is given by,

dNdt=12t+1

Where N is the number of units completed t hours after beginning a new task.

Formula used:

According to the power rule of integrals,

xndx=xn+1n+1+C

Calculation:

As it is provided that for the average new employee, the rate of performance is given by,

dNdt=12t+1

Where N is the number of units completed t hours after beginning a new task.

Now, the function for number of units completed as a function of time t can be obtained by integrating the above rate equation with respect to t as,

dNdtdt=12t+1dt

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