Question

question 30 (3 points)
the table below gives the number of worldwide internet users, in millions, for the years between 1995 and 2007.

year	users (millions)	year	users (millions)
1996	36	2003	719
1997	70	2004	817
1998	147	2005	1018
1999	248	2006	1093
2000	361	2007	1215
2001	536

the cubic function that is the best fit for the data, with ( y ) equal to the number of millions of users and ( x ) equal to the number of years from 1990 is given by ( y = -0.613x^3 + 23.835x^2 - 179.586x + 385.670 ). use the model to predict the number of users in 2010.

• 1360 million
• 1424 million
• 1030 million
• 1215 million

Explanation:

Step1: Determine x for 2010

x is years from 1990. 2010 - 1990 = 20, so x = 20.

Step2: Substitute x=20 into the cubic function

The function is \( y = -0.613x^3 + 23.835x^2 - 179.586x + 385.670 \).
Substitute x = 20:
\( y = -0.613(20)^3 + 23.835(20)^2 - 179.586(20) + 385.670 \)
Calculate each term:

• \( -0.613(8000) = -4904 \)
• \( 23.835(400) = 9534 \)
• \( -179.586(20) = -3591.72 \)
• Constant term: 385.670

Now sum them: \( -4904 + 9534 - 3591.72 + 385.670 \)
First, -4904 + 9534 = 4630
Then, 4630 - 3591.72 = 1038.28
Then, 1038.28 + 385.670 = 1423.95 ≈ 1424

Answer:

1424 million (corresponding to the option: 1424 million)