Number of tickets sold each day for an upcoming performance?

Question

The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x)= -0.6x√2 + 18+ 13 where x is the number of days since the concert was first announced.

Need to know when the ticket sales will peak ___days after the concert was first announced.

The number of tickets sold on that day will be?

Answer 1

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I think there is a problem in your equation, the way you put it, it means that x and N(x) can go indefinitely (no peak). Please check (also it is absurde that you would have 18+13 why not put 21?). However, I think your function is a negative quadratic (which indeed peaks). In that case the function should be:

N(x) = -0.6x^2 + 18x + 13 (where x^2 means x square).

If this is true, let put N(x) = y:

y = -0.6(x^2 - 30x - 13/0.6) = -0.6[(x^2 + 2*(-15)*x + (-15)^2) - (-15)^2 - 13/0.6]

y = -0.6[(x-15)^2 - 148/0.6]

y = -0.6(x-15)^2 + 148

y-148 = -0.6(x-15)^2

You put Y=y-148 and X=x-15, therefore you can write Y=-0.6X (it is a concave parabola). This parabola peaks when X=0. Therefore N(x) peaks when x=15:

"ticket sales will peak _15__days after the concert was first announced"

During the 15th day, the number of daily ticket sold is when Y=0, that is N(x) = y = 148 (otherwise you can find it by replacing x by 15 in N(x) = -0.6x^2 + 18x + 13)