Question

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?

Answer 1

21 times

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:

`x=-(b)/(2a)\\ \\x=-((2)/(3))/(2(-(1)/(63)))\\ \\x=-((2)/(3))/(-(2)/(63))\\\\x=21`

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