Answered

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The effectiveness of a television commercial depends on how many times a viewer watches it. After some experiments an advertising agency found that if the effectiveness E is measured on a scale of 0 to 10, then
E(n) = (2/3)n - (1/63)n²
where n is the number of times a viewer watches a given commercial. For a commercial to have maximum effectiveness, how many times should a viewer watch it?

Sagot :

Answer:

21 times

Step-by-step explanation:

Since the leading coefficient of the expression on the right-hand side is negative, the parabola opens downward, and has a maximum at the vertex. Therefore, we shall determine the x-coordinate of the vertex which will tell us how many times a viewer should watch a commercial for maximum effectiveness:

[tex]x=-\frac{b}{2a}\\ \\x=-\frac{\frac{2}{3}}{2(-\frac{1}{63})}\\ \\x=-\frac{\frac{2}{3}}{-\frac{2}{63}}\\\\x=21[/tex]

Therefore, a viewer would need to watch the commercial 21 times for maximum effectiveness

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