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A Manufacturer of Light Bulbs Wants to Produce Bulbs That F(t)F ( t )

Question 140

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A manufacturer of light bulbs wants to produce bulbs that last about 700 hours but, of course, some bulbs burn out faster than others. Let F(t)F ( t ) be the fraction of the company's bulbs that burn out before tt hours. F(t)F ( t ) lies between 0 and 1 .
Let r(t)=F(t)r ( t ) = F ^ { \prime } ( t ) . What is the value of 0r(t)dt\int _ { 0 } ^ { \infty } r ( t ) d t ?

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