Country Music Cd Sales
How to determine the continuous quadratic function?
12500 copies of a new CD with music are sold during the first week of its release in a certain country. Sales reached a peak 10 weeks later before dwindling to zero sales in week 25.
Determine the continuous quadratic function, S(t), to represent weekly sales, t weeks after the release of the CD.
EDIT:
From the wording of the question, I’m not sure if S(0) = 12500 or S(1)=12500
I tried solving with S(1) = 12500, but got a not so nice result for a (-3125/36)
Assuming first week of release to be t=0 and therefore S(0) = 12500 gives “nicer” results:
Vertex is located at t = 10
One of the roots is located at t = 25 (10+15)
Other root must be located same distance from vertex t = 10-15 = -5
Two roots at -5 and 25
S(t) = a (t + 5) (t – 25)
S(t) = a (t² – 20t – 125)
12,500 copies are sold during first week
S(0) = 12500
a (0 – 0 – 125) = 12500
-125 a = 12500
a = – 12500/125
a = – 100
S(t) = -100 (t² – 20t – 125)
Debra Lyn “I Can’t Remember To Forget You” Unplugged Long Version
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