document.write( "Question 173173This question is from textbook
\n" ); document.write( ": Can someone explain this to me and show step by step so I can have a better understand of this problem thank you so much.\r
\n" ); document.write( "\n" ); document.write( "True or false: The function \"f(x) = 3x\" grows three times faster than the function \"g(x) = x\". Explain. \r
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\n" ); document.write( "\n" ); document.write( "thank you so much
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Algebra.Com's Answer #128052 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'm assuming that the first function is $\"f%28x%29=3%5Ex\"$ \r
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\n" ); document.write( "\n" ); document.write( "Think about it this way. \r
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\n" ); document.write( "\n" ); document.write( "If $\"x=0\"$ , then $\"f%280%29=3%5E0=1\"$ and $\"g%280%29=0\"$ . \r
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\n" ); document.write( "\n" ); document.write( "If $\"x=1\"$ , then $\"f%281%29=3%5E1=3\"$ and $\"g%281%29=3\"$ . \r
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\n" ); document.write( "\n" ); document.write( "If $\"x=2\"$ , then $\"f%282%29=3%5E2=9\"$ and $\"g%282%29=2\"$ . \r
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\n" ); document.write( "\n" ); document.write( "If $\"x=3\"$ , then $\"f%283%29=3%5E3=27\"$ and $\"g%283%29=3\"$ . \r
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\n" ); document.write( "\n" ); document.write( "So we have this table of values\r
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x	f(x)	g(x)
0	1	0
1	3	1
2	9	2
3	27	3

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that $\"g%28x%29\"$ increments by 1 as x increments by 1. On the other hand, we can see that $\"f%28x%29\"$ goes from 1 to 3 (a difference of 2), 3 to 9 (a difference of 6), 9 to 27 (a difference of 18), etc. So the differences between each term is: 2, 6, 18, etc....\r
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\n" ); document.write( "\n" ); document.write( "This means that from x=0 to x=1, the average rate of change for g(x) is 2. From x=1 to x=2, the average rate of change for g(x) is 6. From x=2 to x=3, the average rate of change for f(x) is 18. \r
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\n" ); document.write( "\n" ); document.write( "So dividing the first average rate of change 2 by 1, we get $\"2%2F1=2\"$ . So from x=0 to x=1, $\"f%28x%29\"$ is growing twice as fast as $\"g%28x%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Dividing the second average rate of change 6 by 1, we get $\"6%2F1=6\"$ . So from x=1 to x=2, $\"f%28x%29\"$ is growing six times as fast as $\"g%28x%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Dividing the third average rate of change 18 by 1, we get $\"18%2F1=18\"$ . So from x=2 to x=3, $\"f%28x%29\"$ is growing eighteen times as fast as $\"g%28x%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "As you can see, the exponential function is not growing at a constant rate. So $\"f%28x%29\"$ cannot be growing 3 times faster than $\"g%28x%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Note: the function $\"f%28x%29=3x\"$ does however grow three times faster than $\"g%28x%29=x\"$ , but that is for another problem.\r
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\n" ); document.write( "\n" ); document.write( "So that means that the statement is false. \n" ); document.write( "

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