Question 25: 4 pts
The table shows the number of a particular brand of luxury cars sold in various years. Use a calculator to
write a quartic model for the number of cars sold in a given year since 2000 and use the model to estimate
the number of cars sold in 2005.
Year 2001 2002 2003 2004 2006 2007
Number of cars
705 1716 2803 3515 2742 1081
(thousands)
P(x) = -38.23x3 + 171.56x2 + 869.82x - 329.66
The estimated number of cars sold in 2005 is 3,529.
OP(x) = 21.83x4 – 381.13x2 + 1877.53x2 - 2337.51x + 1533.67
The estimated number of cars sold in 2005 is 2,787.
OP(x) = 6.04x4 - 135.32x3 + 698.78x- 228.48x + 363.95
The estimated number of cars sold in 2005 is 3,551.
OP(x) = -75.46x3 + 420.93x² + 369.82x - 38.33
The estimated number of cars sold in 2005 is 2,901.

The quartic equation that represents the table is: (c) [tex]P(x) = 6.04x^4 - 135.32x^3 + 698.78x^2- 228.48x + 363.95[/tex]
The estimated number of cars sold in 2005 is 3,551.

The table entries are given as:

Year 2001 2002 2003 2004 2006 2007

Cars 705 1716 2803 3515 2742 1081

Represent the table as:

Year 1 2 3 4 6 7

Cars 705 1716 2803 3515 2742 1081

A quartic equation is represented as:

[tex]y = ax^4 + bx^3 + cx + d[/tex]

Using a graphing calculator; we plot the table entries on a graph.

From the graphing calculator, the quartic equation that represents the table is:

[tex]y = 6.04x^4 - 135.32x^3 + 698.78x^2- 228.48x + 363.95[/tex]

Rewrite as a function

[tex]P(x) = 6.04x^4 - 135.32x^3 + 698.78x^2- 228.48x + 363.95[/tex]

Hence, the equation that represents the table is:

(c) [tex]P(x) = 6.04x^4 - 135.32x^3 + 698.78x^2- 228.48x + 363.95[/tex]