Answered

IDNLearn.com is your go-to resource for finding expert answers and community support. Our platform is designed to provide accurate and comprehensive answers to any questions you may have.

The adjacent table gives the number of worldwide Internet users, in millions.

Complete parts (a) through (c).

\begin{tabular}{|c|c|c|c|}
\hline Year & Users (millions) & Year & Users (millions) \\
\hline 1995 & 10 & 2002 & 523 \\
\hline 1996 & 38 & 2003 & 713 \\
\hline 1997 & 75 & 2004 & 820 \\
\hline 1998 & 183 & 2005 & 1043 \\
\hline 1999 & 295 & 2006 & 1099 \\
\hline 2000 & 341 & 2007 & 1216 \\
\hline 2001 & 532 & & \\
\hline
\end{tabular}

(a) Find the cubic function that is the best fit for the data, with [tex]$y$[/tex] equal to the number of millions of users and [tex]$x$[/tex] equal to the number of years from 1990.

[tex]
y=
[/tex]
[tex]\square[/tex] (Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.)

Sagot :

GinnyAnsweridn
To find the cubic function that best fits the given data, we'll use [tex]\( y \)[/tex] to represent the number of millions of users and [tex]\( x \)[/tex] to represent the number of years from 1990.

The given years and corresponding number of users are as follows:

[tex]\[ \begin{array}{|c|c|} \hline \text{Year} & \text{Users (millions)} \\ \hline 1995 & 10 \\ 1996 & 38 \\ 1997 & 75 \\ 1998 & 183 \\ 1999 & 295 \\ 2000 & 341 \\ 2001 & 532 \\ 2002 & 523 \\ 2003 & 713 \\ 2004 & 820 \\ 2005 & 1043 \\ 2006 & 1099 \\ 2007 & 1216 \\ \hline \end{array} \][/tex]

To translate the years into the number of years from 1990, we subtract 1990 from each year:

[tex]\[ \begin{array}{|c|c|} \hline \text{Year} & x = \text{Years from 1990} \\ \hline 1995 & 5 \\ 1996 & 6 \\ 1997 & 7 \\ 1998 & 8 \\ 1999 & 9 \\ 2000 & 10 \\ 2001 & 11 \\ 2002 & 12 \\ 2003 & 13 \\ 2004 & 14 \\ 2005 & 15 \\ 2006 & 16 \\ 2007 & 17 \\ \hline \end{array} \][/tex]

We now need to find the coefficients of the cubic polynomial [tex]\( y = ax^3 + bx^2 + cx + d \)[/tex] that best fits this data. The coefficients can be determined through a method called polynomial regression.

The resulting cubic function that provides the best fit for our data is:

[tex]\[ y = -0.376x^3 + 16.389x^2 - 108.220x + 182.728 \][/tex]

So, the best fit cubic function rounded to three decimal places is:

[tex]\[ y = -0.376x^3 + 16.389x^2 - 108.220x + 182.728 \][/tex]
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions find clarity at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.