SOLUTION: the number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x)=-0.4x^+8x+14, when will the daily ticket sales peak and how many tickets will b

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: the number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x)=-0.4x^+8x+14, when will the daily ticket sales peak and how many tickets will b      Log On


   

Question 536477: the number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x)=-0.4x^+8x+14, when will the daily ticket sales peak and how many tickets will be sold that day? Ticket sales will peak how many days after the concert was first announced and how many tickets were sold on that day?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x+=+1+, +N%281%29+ 1st day and sales for 1st day
+x+=+2+, +N%282%29+ 2nd day and sales for 2nd day
+x+=+3+, +N%283%29+ 3rd day and sales for 3rd day
etc . . .
+N%28x%29=-.4x%5E2+%2B+8x+%2B+14+
The minus in front of the x-squared term tells me
that +N%28x%29+ has a max and not a min.
The max, or vertex, of a parabola is at +x%5Bmax%5D+=+-b%2F%282a%29+
+a+=+-.4+
+b+=+8+
+x%5Bmax%5D+=+-8%2F%282%2A%28-.4%29%29+
+x%5Bmax%5D+=+-8%2F-.8+
+x%5Bmax%5D+=+10+
Now find +N%2810%29+
+N%2810%29+=+-.4%2A10%5E2+%2B+8%2A10+%2B+14+
+N%2810%29+=+-40+%2B+80+%2B+14+
+N%2810%29+=+54+
The max daily ticket sales occur 10 days after concert
is announced and the sales on the 10th day are $54
-----------------------
To check to see if this is the max, find +N%289.9%29+
and +N%2810.1%29+. They should both be slightly less
than +54+