THE POLITICAL NOISE PROBLEM:
The amount of background noise is important to television news reporters. One station developed the formula
N= -t2 + 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? Can you explain this please??
The greatest? Plot the equation, and see when it peaks.
I'm still learning how to plot on my TI 83 plus..can you guide me?
To find the number of seconds after the speaker stops that corresponds to the greatest noise level, we need to analyze the given formula. The formula is N = -t^2 + 12t + 54, where N represents the noise level in decibels and t represents the time after the speaker stops talking in seconds.
To find the maximum value of the noise level (N), we can make use of calculus. The maximum value occurs at the vertex of the parabola defined by the equation.
The vertex of a parabola can be found using the formula t = -b/2a, where a and b are the coefficients of the quadratic equation, N = at^2 + bt + c.
Comparing the given formula N = -t^2 + 12t + 54 with the general form of a quadratic equation, we can see that a = -1 and b = 12.
Substituting these values into the formula t = -b/2a, we have:
t = -12 / (2 * -1)
t = -12 / -2
t = 6
According to the formula, the greatest noise level will occur 6 seconds after the speaker stops.