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Math Help - Question about e^2x graph

  1. #1
    Junior Member freestar's Avatar
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    Question about e^2x graph

    Use a graph produced by your calculator to estima the values of x for which e^2^x is smaller than (x-8)^4. Also, describe clearly and accurately the purpose of each needed step.

    This is what I tried but I am totally lost because I can't figure out how to approach this:
    e^2^x<(x-8)^4

    I could take the 4th root of both sides but I can't isolate x. Not too sure how to solve this question.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Question about e^2x graph

    But beside the excercice you need the graphs of the functions, so have you tried to solve this exercice with the calculator? ...
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  3. #3
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    Re: Question about e^2x graph

    Try e^{2x}- (x-8)^4 where are the zeros?
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  4. #4
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    e^(i*pi)'s Avatar
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    Re: Question about e^2x graph

    Quote Originally Posted by freestar View Post
    Use a graph produced by your calculator to estima the values of x for which e^2^x is smaller than (x-8)^4. Also, describe clearly and accurately the purpose of each needed step.

    This is what I tried but I am totally lost because I can't figure out how to approach this:
    e^2^x<(x-8)^4

    I could take the 4th root of both sides but I can't isolate x. Not too sure how to solve this question.
    It says use a calculator for that reason - plot both graphs on the same axes and pick the appropriate values.

    You know that (x-8)^4 \geq 0 and that the points (0,8^4) and (8,0) lie on it.
    You know that e^{2x} has the x-axis as an asymptote and the point (0,1) lies on it.

    Here is the wolfram plot, I have limited the domain to make it easier to see: plot &#123;y&#61;e&#94;&#40;2x&#41;,y&#61;&#40;x-8&#41;&#94;4&#125; between 0 and 5 - Wolfram|Alpha
    Last edited by e^(i*pi); September 11th 2011 at 03:19 PM. Reason: tag fix
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  5. #5
    Junior Member freestar's Avatar
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    Re: Question about e^2x graph

    Quote Originally Posted by e^(i*pi) View Post
    It says use a calculator for that reason - plot both graphs on the same axes and pick the appropriate values.

    You know that (x-8)^4 \geq 0 and that the points (0,8^4) and (8,0) lie on it.
    You know that e^{2x} has the x-axis as an asymptote and the point (0,1) lies on it.

    Here is the wolfram plot, I have limited the domain to make it easier to see: http://www.wolframalpha.com/input/?i=plot+{y%3De^%282x%29%2Cy%3D%28x-8%29^4}+between+0+and+5
    So in that case, x\leq3.155633123?
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Question about e^2x graph

    Correct!
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  7. #7
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    e^(i*pi)'s Avatar
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    Re: Question about e^2x graph

    Quote Originally Posted by freestar View Post
    So in that case, x\leq3.155633123?
    I'd say so, it agrees with the general value of the plot and I assume your calculator spat it out
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