<PRE><B>Question 156297</B>
# 4





Let&#39;s find the function value when {{{x=1}}}:



{{{y=10^x}}} Start with the given equation.



{{{y=10^(1)}}} Plug in {{{x=1}}}.



{{{y=10}}} Raise 10 to the first power to get 10



So if {{{x=1}}}, then {{{y=10}}}.


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Let&#39;s find the function value when {{{x=2}}}:



{{{y=10^x}}} Start with the given equation.



{{{y=10^(2)}}} Plug in {{{x=2}}}.



{{{y=100}}} Raise 10 to the second power to get 100



So if {{{x=2}}}, then {{{y=100}}}.


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Let&#39;s find the function value when {{{x=4}}}:



{{{y=10^x}}} Start with the given equation.



{{{y=10^(4)}}} Plug in {{{x=4}}}.



{{{y=10000}}} Raise 10 to the 4th power to get 10,000




So if {{{x=4}}}, then {{{y=10000}}}.


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Let&#39;s find the function value when {{{x=8}}}:



{{{y=10^x}}} Start with the given equation.



{{{y=10^(8)}}} Plug in {{{x=8}}}.



{{{y=100000000}}} Raise 10 to the 8th power to get 100,000,000



So if {{{x=8}}}, then {{{y=100000000}}}.


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Let&#39;s find the function value when {{{x=16}}}:



{{{y=10^x}}} Start with the given equation.



{{{y=10^(16)}}} Plug in {{{x=16}}}.



{{{y=1*10^16}}} Raise 10 to the 16th power to get {{{1*10^16}}} (this is a 1 followed by 16 zeros)




So if {{{x=16}}}, then {{{y=1*10^16}}}.


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Now let&#39;s make a table of the values we just found.



&lt;h4&gt;Table of Values:&lt;/h4&gt;&lt;pre&gt;

&lt;TABLE border=&quot;1&quot; width=&quot;100&quot;&gt;
&lt;TR&gt;&lt;TD&gt;x&lt;/TD&gt;&lt;TD&gt;y&lt;/TD&gt;&lt;/TR&gt;&lt;tr&gt;&lt;td&gt;1&lt;/td&gt;&lt;td&gt;10&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td&gt;2&lt;/td&gt;&lt;td&gt;100&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td&gt;4&lt;/td&gt;&lt;td&gt;10,000&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td&gt;8&lt;/td&gt;&lt;td&gt;100,000,000&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td&gt;16&lt;/td&gt;&lt;td&gt;1*10^16&lt;/td&gt;&lt;/tr&gt;
&lt;/TABLE&gt;

&lt;/pre&gt;



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.

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