The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x)=-0.6x^2+12+13, 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?
N(x) = -0.6x^x+12x+13.
The above is the Eq of a parabola that
opens downwrd. Therefore, the max point
on the curve is the vertex:
Xv = -b/2a = -12 / -1.2 = 10 = The # of days.
In the original Eq, substitute 10 for
X to get # of tickets sold:
N(x) = (-0.6)10^2 + 12*10 + 13 = 73. =
The # of tickets sold.
To find out when the daily ticket sales will peak and the corresponding number of tickets sold on that day, we need to find the vertex of the quadratic function N(x) = -0.6x^2 + 12x + 13.
The vertex of a quadratic function in the form of ax^2 + bx + c can be found using the formula x = -b / (2a). In this case, a = -0.6 and b = 12.
x = -12 / (2 * (-0.6))
x = -12 / (-1.2)
x = 10
Therefore, the daily ticket sales will peak on the 10th day since the concert was first announced.
To find the number of tickets sold on that day, we substitute x = 10 into the N(x) equation.
N(10) = -0.6(10)^2 + 12(10) + 13
N(10) = -0.6(100) + 120 + 13
N(10) = -60 + 120 + 13
N(10) = 73
Therefore, on the 10th day, there will be a peak in ticket sales and 73 tickets will be sold that day.