II. Suppose that the total worldwide sales for a song album are approximated by the function: 150x³ x³ +8 where, S(x) = S(x) is the measured in millions of dollars; and x is the number of months since the album is released A. Use a graphing tool to show the graph of S(x) in the context of the situation. B. Construct a table to show the total number of sales for the first two years since the album's release. C. What will be the album's gross sales in the long run? Support your answer analytically using the concept of limits.
II. Suppose that the total worldwide sales for a song album are approximated by the function: 150x³ x³ +8 where, S(x) = S(x) is the measured in millions of dollars; and x is the number of months since the album is released A. Use a graphing tool to show the graph of S(x) in the context of the situation. B. Construct a table to show the total number of sales for the first two years since the album's release. C. What will be the album's gross sales in the long run? Support your answer analytically using the concept of limits.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:II. Suppose that the total worldwide sales for a song album are approximated by the function:
150x³
x³ +8
where,
S(x) =
S(x) is the measured in millions of dollars; and
x is the number of months since the album is released
A. Use a graphing tool to show the graph of S(x) in the context of the situation.
B. Construct a table to show the total number of sales for the first two years since the album's release.
C. What will be the album's gross sales in the long run? Support your answer analytically using the concept
of limits.
D. Based on A, B, and C, discuss the trend of the gross sales of the album.
Consider the function (for questions E and F)
S(x): =
x →∞0
E. What will happen to lim S(x) if k is replaced by any value greater than 8? Any value less than 8? Discuss
how the number k affects the limit of S(x) as x gets very large. Support your answer graphically to
show the variation.
F. What will happen to lim S(x) if 150 is replaced by any constant? Support your answer analytically.
x→∞0
Consider the function (for question G)
150x³
x³ + k
S(x) =
ax³
bx³ + k
G. What will happen to lim S(x) if a, b, and k are any constant? Support your answer analytically. How do
the constants a, b, and k affect the total monthly gross sales of the album?
X80
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