Hello please help tutors have given different solutions please help give a certain and correct one please thank you

Question

1.) Use finite differences to identify the degree of the polynomial that best describes the data.

 

`A.) quartic

B.) quintic

C.) quadratic

D.) cubic

 

2.) 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.

 

 

A.) P(x) ≈ −38.23x3 + 56.86x2 + 1098.23x + 557.48

The estimated number of cars sold in 2005 is 2,691.

 

B.) P(x) ≈ 6.04x4 − 135.32x3 + 698.78x2 − 228.48x + 247.95

The estimated number of cars sold in 2005 is 3,432.

 

C.) P(x) ≈ 6.04x4 − 111.18x3 + 329.04x2 + 787.26x + 588.97

The estimated number of cars sold in 2005 is 2,626.

 

D.) P(x) ≈ −38.23x3 + 56.86x2 + 1098.23x + 557.48

The estimated number of cars sold in 2005 is 3,413.

 

Answer 1

a) Take the 1st difference (of the y-values), then the 2nd difference, then the 3rd difference, then the 4th difference like this:

You see that you must go to the 4th difference before the difference values are the same. So it is a 4th order polynomial (i.e., quartic)

For b) just plug in the data (using x = 1, 2, 3, 4, 6, 7 instead of 2001, etc) into a list in your TI-84 and execute "stat" "calc" "quartreg" and you get:

P(x) = 6.035x⁴ - 135.3166667x³ + 698.775x² - 228.4761905x + 247.9542857

The P(5) = 3432