   Chapter 7.8, Problem 67E

Chapter
Section
Textbook Problem

# A manufacturer of lightbulbs wants to produce bulbs that last about 700 hours but, of course, some bulbs burn out faster than others. Let F(t) be the fraction of the company’s bulbs that burn out before t hours, so F(t) always lies between 0 and 1.(a) Make a rough sketch of what you think the graph of F might look like.(b) What is the meaning of the derivative r ( t ) = F ′ ( t ) ?(c) What is the value of ∫ 0 ∞ r ( t )   d t Why?

To determine

(a)

To make:

A rough sketch of the graph of F

Explanation

Given:

Life of bulbs is 700 hours

F(t) be the fraction of bulbs that burn out before t hours

The graph of F(t) is the fraction of bulbs that will burn out by time t

To determine

(b)

To write:

The meaning of the derivative r(t)=F(t).

To determine

(c)

The value of 0r(t)dt.

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