document.write( "Question 156297: 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. \r
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\n" ); document.write( "\n" ); document.write( "4. f(x) = 10^x \r
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Algebra.Com's Answer #115098 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
# 4\r
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\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=1\"$ :\r
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\n" ); document.write( "\n" ); document.write( " $\"y=10%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=10%5E%281%29\"$ Plug in $\"x=1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=10\"$ Raise 10 to the first power to get 10\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=1\"$ , then $\"y=10\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=2\"$ :\r
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\n" ); document.write( "\n" ); document.write( " $\"y=10%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=10%5E%282%29\"$ Plug in $\"x=2\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=100\"$ Raise 10 to the second power to get 100\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=2\"$ , then $\"y=100\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=4\"$ :\r
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\n" ); document.write( "\n" ); document.write( " $\"y=10%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=10%5E%284%29\"$ Plug in $\"x=4\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=10000\"$ Raise 10 to the 4th power to get 10,000\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=4\"$ , then $\"y=10000\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=8\"$ :\r
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\n" ); document.write( "\n" ); document.write( " $\"y=10%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=10%5E%288%29\"$ Plug in $\"x=8\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=100000000\"$ Raise 10 to the 8th power to get 100,000,000\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=8\"$ , then $\"y=100000000\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=16\"$ :\r
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\n" ); document.write( "\n" ); document.write( " $\"y=10%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=10%5E%2816%29\"$ Plug in $\"x=16\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%2A10%5E16\"$ Raise 10 to the 16th power to get $\"1%2A10%5E16\"$ (this is a 1 followed by 16 zeros)\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=16\"$ , then $\"y=1%2A10%5E16\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now let's make a table of the values we just found.\r
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Table of Values:

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document.write( "x y
1 10
2 100
4 10,000
8 100,000,000
16 1*10^16\r\n" );
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\n" ); document.write( "\n" ); document.write( "Since we are dealing with an exponential function, this means that the function undergoes exponential growth. This is the fastest of all of the growth rates in this group.\r
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