document.write( "Question 150910: Hello all I would like your help one more time. I've got most of what my teacher asked us to do but I am stuck on the following the task is to:\r
\n" ); document.write( "\n" ); document.write( "Evaluate the functions for the values of x given as 1, 2, 4, 8, and 16. Describe the differences in the rate at which each function changes with increasing values of x. f(x) = x2 - 3x + 2
\n" ); document.write( "f(x) = 2x3 + 7x2 - x - 1
\n" ); document.write( "f(x) = 10x
\n" ); document.write( "f(x) = ln x (I don't know if this is (one n x) or the letter (l)n x, whatever that means)\r
\n" ); document.write( "\n" ); document.write( "Any help would be GREATLY appreciated!!
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #110846 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
# 1\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=1\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-3x%2B2\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=%281%29%5E2-3%281%29%2B2\"$ Plug in $\"x=1\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1%281%29-3%281%29%2B2\"$ Square $\"1\"$ to get $\"1\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1-3%281%29%2B2\"$ Multiply $\"1\"$ and $\"1\"$ to get $\"1\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1-3%2B2\"$ Multiply $\"-3\"$ and $\"1\"$ to get $\"-3\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=0\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=1\"$ , then $\"y=0\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=2\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-3x%2B2\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=%282%29%5E2-3%282%29%2B2\"$ Plug in $\"x=2\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1%284%29-3%282%29%2B2\"$ Square $\"2\"$ to get $\"4\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=4-3%282%29%2B2\"$ Multiply $\"1\"$ and $\"4\"$ to get $\"4\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=4-6%2B2\"$ Multiply $\"-3\"$ and $\"2\"$ to get $\"-6\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=0\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=2\"$ , then $\"y=0\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=4\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-3x%2B2\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=%284%29%5E2-3%284%29%2B2\"$ Plug in $\"x=4\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1%2816%29-3%284%29%2B2\"$ Square $\"4\"$ to get $\"16\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=16-3%284%29%2B2\"$ Multiply $\"1\"$ and $\"16\"$ to get $\"16\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=16-12%2B2\"$ Multiply $\"-3\"$ and $\"4\"$ to get $\"-12\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=6\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=4\"$ , then $\"y=6\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=8\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-3x%2B2\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=%288%29%5E2-3%288%29%2B2\"$ Plug in $\"x=8\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1%2864%29-3%288%29%2B2\"$ Square $\"8\"$ to get $\"64\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=64-3%288%29%2B2\"$ Multiply $\"1\"$ and $\"64\"$ to get $\"64\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=64-24%2B2\"$ Multiply $\"-3\"$ and $\"8\"$ to get $\"-24\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=42\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=8\"$ , then $\"y=42\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=16\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-3x%2B2\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=%2816%29%5E2-3%2816%29%2B2\"$ Plug in $\"x=16\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1%28256%29-3%2816%29%2B2\"$ Square $\"16\"$ to get $\"256\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=256-3%2816%29%2B2\"$ Multiply $\"1\"$ and $\"256\"$ to get $\"256\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=256-48%2B2\"$ Multiply $\"-3\"$ and $\"16\"$ to get $\"-48\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=210\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=16\"$ , then $\"y=210\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let's make a table of the values we just found.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Jump to Top of Page\r
\n" ); document.write( "\n" ); document.write( "

Table of Values:

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "x y
1 0
2 0
4 6
8 42
16 210\r\n" );
document.write( "\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "# 2\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=1\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2x%5E3%2B7x%5E2-x-1\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%281%29%5E3%2B7%281%29%5E2-1-1\"$ Plug in $\"x=1\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%281%29%2B7%281%29%5E2-1-1\"$ Cube $\"1\"$ to get $\"1\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%281%29%2B7%281%29-1-1\"$ Square $\"1\"$ to get $\"1\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%2B7%281%29-1-1\"$ Multiply $\"2\"$ and $\"1\"$ to get $\"2\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%2B7-1-1\"$ Multiply $\"7\"$ and $\"1\"$ to get $\"7\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=7\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=1\"$ , then $\"y=7\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=2\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2x%5E3%2B7x%5E2-x-1\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%282%29%5E3%2B7%282%29%5E2-2-1\"$ Plug in $\"x=2\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%288%29%2B7%282%29%5E2-2-1\"$ Cube $\"2\"$ to get $\"8\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%288%29%2B7%284%29-2-1\"$ Square $\"2\"$ to get $\"4\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=16%2B7%284%29-2-1\"$ Multiply $\"2\"$ and $\"8\"$ to get $\"16\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=16%2B28-2-1\"$ Multiply $\"7\"$ and $\"4\"$ to get $\"28\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=41\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=2\"$ , then $\"y=41\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=4\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2x%5E3%2B7x%5E2-x-1\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%284%29%5E3%2B7%284%29%5E2-4-1\"$ Plug in $\"x=4\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%2864%29%2B7%284%29%5E2-4-1\"$ Cube $\"4\"$ to get $\"64\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%2864%29%2B7%2816%29-4-1\"$ Square $\"4\"$ to get $\"16\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=128%2B7%2816%29-4-1\"$ Multiply $\"2\"$ and $\"64\"$ to get $\"128\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=128%2B112-4-1\"$ Multiply $\"7\"$ and $\"16\"$ to get $\"112\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=235\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=4\"$ , then $\"y=235\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=8\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2x%5E3%2B7x%5E2-x-1\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%288%29%5E3%2B7%288%29%5E2-8-1\"$ Plug in $\"x=8\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%28512%29%2B7%288%29%5E2-8-1\"$ Cube $\"8\"$ to get $\"512\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%28512%29%2B7%2864%29-8-1\"$ Square $\"8\"$ to get $\"64\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1024%2B7%2864%29-8-1\"$ Multiply $\"2\"$ and $\"512\"$ to get $\"1024\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1024%2B448-8-1\"$ Multiply $\"7\"$ and $\"64\"$ to get $\"448\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1463\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=8\"$ , then $\"y=1463\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=16\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2x%5E3%2B7x%5E2-x-1\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%2816%29%5E3%2B7%2816%29%5E2-16-1\"$ Plug in $\"x=16\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%284096%29%2B7%2816%29%5E2-16-1\"$ Cube $\"16\"$ to get $\"4096\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%284096%29%2B7%28256%29-16-1\"$ Square $\"16\"$ to get $\"256\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=8192%2B7%28256%29-16-1\"$ Multiply $\"2\"$ and $\"4096\"$ to get $\"8192\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=8192%2B1792-16-1\"$ Multiply $\"7\"$ and $\"256\"$ to get $\"1792\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=9967\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=16\"$ , then $\"y=9967\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let's make a table of the values we just found.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

Table of Values:

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "x y
1 7
2 41
4 235
8 1463
16 9967\r\n" );
document.write( "\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "# 3\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=1\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=10x\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=10%281%29\"$ Plug in $\"x=1\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=10\"$ Multiply $\"10\"$ and $\"1\"$ to get $\"10\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=10\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=1\"$ , then $\"y=10\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=2\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=10x\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=10%282%29\"$ Plug in $\"x=2\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=20\"$ Multiply $\"10\"$ and $\"2\"$ to get $\"20\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=20\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=2\"$ , then $\"y=20\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=4\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=10x\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=10%284%29\"$ Plug in $\"x=4\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=40\"$ Multiply $\"10\"$ and $\"4\"$ to get $\"40\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=40\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=4\"$ , then $\"y=40\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=8\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=10x\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=10%288%29\"$ Plug in $\"x=8\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=80\"$ Multiply $\"10\"$ and $\"8\"$ to get $\"80\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=80\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=8\"$ , then $\"y=80\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=16\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=10x\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=10%2816%29\"$ Plug in $\"x=16\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=160\"$ Multiply $\"10\"$ and $\"16\"$ to get $\"160\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=160\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=16\"$ , then $\"y=160\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let's make a table of the values we just found.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

Table of Values:

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "x y
1 10
2 20
4 40
8 80
16 160\r\n" );
document.write( "\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "# 4\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Note: ln(x) also looks like LN(x) (to pronounce it, simply read off the letters \"L\" \"N\")\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "This is the natural log of x. So it is a logarithmic function.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=1\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=ln%28x%29\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=ln%281%29\"$ Plug in $\"x=1\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=0\"$ Take the natural log of 1 to get 0\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , $\"y=0\"$ . \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "----------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=2\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=ln%28x%29\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=ln%282%29\"$ Plug in $\"x=2\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=0.693\"$ Take the natural log of 2 to get 0.693\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , $\"y=0.693\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "----------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=4\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=ln%28x%29\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=ln%284%29\"$ Plug in $\"x=4\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1.386\"$ Take the natural log of 4 to get 1.386\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=4\"$ , $\"y=1.386\"$ . \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=8\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=ln%28x%29\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=ln%288%29\"$ Plug in $\"x=8\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2.079\"$ Take the natural log of 8 to get 2.079\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=8\"$ , $\"y=2.079\"$ . \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=16\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=ln%28x%29\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=ln%2816%29\"$ Plug in $\"x=16\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2.773\"$ Take the natural log of 16 to get 2.773\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=16\"$ , $\"y=2.773\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let's make a table of the values we just found.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

Table of Values:

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "x y
1 0
2 0.693
4 1.386
8 2.079
16 2.773\r\n" );
document.write( "\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "===========================================================\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So to compare the rates, simply compare the tables:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Table for $\"y=x%5E2-3x%2B2\"$ \r
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "x y
1 0
2 0
4 6
8 42
16 210\r\n" );
document.write( "\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Table for $\"y=2x%5E3%2B7x%5E2-x-1\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "x y
1 7
2 41
4 235
8 1463
16 9967\r\n" );
document.write( "\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Table for $\"y=10x\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "x y
1 10
2 20
4 40
8 80
16 160\r\n" );
document.write( "\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Table for $\"y=ln%28x%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "x y
1 0
2 0.693
4 1.386
8 2.079
16 2.773\r\n" );
document.write( "\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "From the tables, the functions can be sorted from slowest growing to fastest growing like this:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=ln%28x%29\"$ , $\"y=10x\"$ , $\"y=x%5E2-3x%2B2\"$ , and $\"y=2x%5E3%2B7x%5E2-x-1\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So $\"y=ln%28x%29\"$ is the slowest growing function and $\"y=2x%5E3%2B7x%5E2-x-1\"$ is the fastest growing function.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If all of that is confusing, simply graph all of the functions to get\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

Graph of $\"y=x%5E2-3x%2B2\"$ (red), $\"y=2x%5E3%2B7x%5E2-x-1\"$ (green), $\"y=10x\"$ (blue), and $\"y=ln%28x%29\"$ (purple)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "From the graph, we can see that the order from slowest growing to fastest growing is\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=ln%28x%29\"$ , $\"y=10x\"$ , $\"y=x%5E2-3x%2B2\"$ , and $\"y=2x%5E3%2B7x%5E2-x-1\"$
\n" ); document.write( " \n" ); document.write( "

\n" );