Question 156295
# 3


Let's find the function value when {{{x=1}}}:



{{{y=2x^3+7x^2-x-1}}} Start with the given equation.



{{{y=2(1)^3+7(1)^2-1-1}}} Plug in {{{x=1}}}.



{{{y=2(1)+7(1)^2-1-1}}} Cube {{{1}}} to get {{{1}}}.



{{{y=2(1)+7(1)-1-1}}} Square {{{1}}} to get {{{1}}}.



{{{y=2+7(1)-1-1}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}.



{{{y=2+7-1-1}}} Multiply {{{7}}} and {{{1}}} to get {{{7}}}.



{{{y=7}}} Combine like terms.



So if {{{x=1}}}, then {{{y=7}}}.


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Let's find the function value when {{{x=2}}}:



{{{y=2x^3+7x^2-x-1}}} Start with the given equation.



{{{y=2(2)^3+7(2)^2-2-1}}} Plug in {{{x=2}}}.



{{{y=2(8)+7(2)^2-2-1}}} Cube {{{2}}} to get {{{8}}}.



{{{y=2(8)+7(4)-2-1}}} Square {{{2}}} to get {{{4}}}.



{{{y=16+7(4)-2-1}}} Multiply {{{2}}} and {{{8}}} to get {{{16}}}.



{{{y=16+28-2-1}}} Multiply {{{7}}} and {{{4}}} to get {{{28}}}.



{{{y=41}}} Combine like terms.



So if {{{x=2}}}, then {{{y=41}}}.


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Let's find the function value when {{{x=4}}}:



{{{y=2x^3+7x^2-x-1}}} Start with the given equation.



{{{y=2(4)^3+7(4)^2-4-1}}} Plug in {{{x=4}}}.



{{{y=2(64)+7(4)^2-4-1}}} Cube {{{4}}} to get {{{64}}}.



{{{y=2(64)+7(16)-4-1}}} Square {{{4}}} to get {{{16}}}.



{{{y=128+7(16)-4-1}}} Multiply {{{2}}} and {{{64}}} to get {{{128}}}.



{{{y=128+112-4-1}}} Multiply {{{7}}} and {{{16}}} to get {{{112}}}.



{{{y=235}}} Combine like terms.



So if {{{x=4}}}, then {{{y=235}}}.


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Let's find the function value when {{{x=8}}}:



{{{y=2x^3+7x^2-x-1}}} Start with the given equation.



{{{y=2(8)^3+7(8)^2-8-1}}} Plug in {{{x=8}}}.



{{{y=2(512)+7(8)^2-8-1}}} Cube {{{8}}} to get {{{512}}}.



{{{y=2(512)+7(64)-8-1}}} Square {{{8}}} to get {{{64}}}.



{{{y=1024+7(64)-8-1}}} Multiply {{{2}}} and {{{512}}} to get {{{1024}}}.



{{{y=1024+448-8-1}}} Multiply {{{7}}} and {{{64}}} to get {{{448}}}.



{{{y=1463}}} Combine like terms.



So if {{{x=8}}}, then {{{y=1463}}}.


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Let's find the function value when {{{x=16}}}:



{{{y=2x^3+7x^2-x-1}}} Start with the given equation.



{{{y=2(16)^3+7(16)^2-16-1}}} Plug in {{{x=16}}}.



{{{y=2(4096)+7(16)^2-16-1}}} Cube {{{16}}} to get {{{4096}}}.



{{{y=2(4096)+7(256)-16-1}}} Square {{{16}}} to get {{{256}}}.



{{{y=8192+7(256)-16-1}}} Multiply {{{2}}} and {{{4096}}} to get {{{8192}}}.



{{{y=8192+1792-16-1}}} Multiply {{{7}}} and {{{256}}} to get {{{1792}}}.



{{{y=9967}}} Combine like terms.



So if {{{x=16}}}, then {{{y=9967}}}.


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Now let's make a table of the values we just found.




<h4>Table of Values:</h4><pre>

<TABLE border="1" width="100">
<TR><TD>x</TD><TD>y</TD></TR><tr><td>1</td><td>7</td></tr>
<tr><td>2</td><td>41</td></tr>
<tr><td>4</td><td>235</td></tr>
<tr><td>8</td><td>1463</td></tr>
<tr><td>16</td><td>9967</td></tr>
</TABLE>

</pre>


Since this polynomial is a cubic, this tells us that the rate of growth is cubic growth. This growth rate is larger than quadratic growth.