The number of tickets sold each day for an upcoming performance of Handel,s Messiah is given by N(x)=-0.4^2+8.8x+10, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will be sold that day?
you know that ax^2+bx+c has its vertex at x = -b/2a.
Here, that means the vertex (maximum no. tickets) occurs at x = 11 days
To find when the daily ticket sales will peak and how many tickets will be sold on that day, we need to determine the maximum point of the given function N(x).
The given function is:
N(x) = -0.4x^2 + 8.8x + 10
To find the maximum point, we need to consider the quadratic equation in the form ax^2 + bx + c, where a = -0.4, b = 8.8, and c = 10.
The x-coordinate of the maximum point can be found using the formula:
x = -b / (2a)
Substituting the values, we have:
x = -8.8 / (2 * -0.4)
Simplifying, we get:
x = -8.8 / -0.8
x = 11
Therefore, the peak in daily ticket sales will occur on the 11th day since the concert's announcement.
To find the number of tickets sold on that day, substitute x = 11 in the given function:
N(11) = -0.4(11)^2 + 8.8(11) + 10
Calculating, we get:
N(11) = -0.4(121) + 96.8 + 10
N(11) = -48.4 + 96.8 + 10
N(11) = 58.4
Hence, on the 11th day, the daily ticket sales will peak and 58 tickets will be sold on that day.