A manufacturer of lightbulbs wants to produce bulbs thatlast about 700 hours but, of course, some bulbs burn outfaster than others. Let F (t) be the fraction of the company’sbulbs that burn out before hours, so F (t) always liesbetween 0 and 1.(a) Make a rough sketch of what you think the graph of Fmight look like.(b) What is the meaning of the derivative r(t) = F ' (t) ?(c) What is the value of integral 0 to infinity r(t) dt ? Why?
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
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 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 integral 0 to infinity r(t) dt ? Why?
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