   Chapter 12, Problem 36RE ### 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 Suppose that the rate of change of production of the average worker at a factory is given by d p d t =   27   +   24 t   −   3 t 2 ,   0   ≤ t ≤   8 where p is the number of units the worker produces in t hours. How many units will the average worker produce in an 8-hour shift? (Assume that p = 0 when t = 0.)

To determine

To calculate: The number of units the worker produce in an 8 hour shift where at a factory, the rate of change of production of an average worker is given by dpdt=27+24t3t2 for 0t8 and p is the number of units the worker produces in t hours.

Explanation

Given information:

It is provided that the rate of change of production of the average worker at a factory is dpdt=27+24t3t2.

Formula used:

The number of units produced is given by the integral of the rate of change of production,

p(t)=dpdtdt

Calculation:

Consider the provided equation,

dpdt=27+24t3t2

Use the formula of production to calculate the number of units produced as,

p(t)=(27+24t3t2)dt=(27)dt+(24t)dt+(3t2)dt+C=27t+24t223<

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 