Question

use the table feature of a graphing calculator to do this exercise. the value (in millions of dollars) of new orders for all manufacturing industries can be approximated by the function $h(x) = -5.32x^3 + 48.9x^2 + 20.6x + 4123$, where $x = 0$ corresponds to the year 2000. create a table that gives the value of the sales for the years 2002 - 2007. complete the table below | year | x | h(x) | | 2002 | □ | □ |

Explanation:

Step1: Determine x for 2002

Since \( x = 0 \) corresponds to 2000, for 2002, \( x=2002 - 2000=2 \).

Step2: Substitute x = 2 into h(x)

The function is \( h(x)=- 5.32x^{3}+48.9x^{2}+20.6x + 4123 \).
Substitute \( x = 2 \):

$$
LATEXBLOCK0
$$

For the years 2003 - 2007:

• 2003: \( x = 3 \)

$$
LATEXBLOCK1
$$

• 2004: \( x = 4 \)

$$
LATEXBLOCK2
$$

• 2005: \( x = 5 \)

$$
LATEXBLOCK3
$$

• 2006: \( x = 6 \)

$$
LATEXBLOCK4
$$

• 2007: \( x = 7 \)

$$
LATEXBLOCK5
$$

Answer:

Year	x	h(x) (in millions of dollars)
2003	3	4481.26
2004	4	4647.32
2005	5	4783.5
2006	6	4857.88
2007	7	4838.54

For the 2002 row specifically:

• x: 2
• h(x): 4317.24