SOLUTION: The amount of background noise is important to television news reporters. One station developed the formula n= -t^2 + 12t +54 showing the noise level in decibels (N) as it relates

Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> SOLUTION: The amount of background noise is important to television news reporters. One station developed the formula n= -t^2 + 12t +54 showing the noise level in decibels (N) as it relates       Log On

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Question 288215: The amount of background noise is important to television news reporters. One station developed the formula n= -t^2 + 12t +54 showing the noise level in decibels (N) as it relates to the time after the speaker stops talking in seconds (t). How many seconds after the speaker stops will the noise level
be the greatest? Write and tell how you decided.
Answer by amnd(23) About Me  (Show Source):
You can put this solution on YOUR website!
You can find the amount of seconds (t) that would lead to the maximum noise level (N) by finding its derivative through differentiation, or N'. At maximum N, N' would have a value of zero.
For N+=+-t%5E2+%2B+12t+%2B54, N'=-2t+12
As N'=0:
-2t+12=0, yielding t = 6 seconds
You can try inputting various values for t and compare them (for example, 5, 6 and 7), and it would yield the same result.