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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^\prime (t) $?

(c) What is the value of $ \displaystyle \int_0^\infty r(t)\ dt $? Why?

a.

b. $r(t)=F^{\prime}(t)$ is the rate at which the fraction $F(t)$ of burnt-out bulbs increases as t increasees. This could be interpreted as a fractional burnout rate.

c. 1

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