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Math Help - Finding Intersections of Polynomial and Exponential Functions

  1. #1
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    Finding Intersections of Polynomial and Exponential Functions

    Hi. I'm looking for some general tips for solving equations that I'm running into as I study for the Math GRE Subject test. For example, I have a problem where I have to find the intersection of y=x^{12} and y=2^{x}, and another where I need to find the intersection of y=10x and y=e^{x}. Usually, one function is some sort of polynomial and the other is an exponential function. I don't even know what subject this falls under, so I'm not sure what sorts of textbooks to look into. Often, the questions just ask how many points of intersection there are, as opposed to what the values are, so maybe there is some sort of method for that that I don't know about.

    Thanks.
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    Quote Originally Posted by StarKid View Post
    Hi. I'm looking for some general tips for solving equations that I'm running into as I study for the Math GRE Subject test. For example, I have a problem where I have to find the intersection of y=x^{12} and y=2^{x}, and another where I need to find the intersection of y=10x and y=e^{x}. Usually, one function is some sort of polynomial and the other is an exponential function. I don't even know what subject this falls under, so I'm not sure what sorts of textbooks to look into. Often, the questions just ask how many points of intersection there are, as opposed to what the values are, so maybe there is some sort of method for that that I don't know about.

    Thanks.
    Can't be done with algebra (unless you have learned about the Lambert W-function, which I doubt you have). This sorts of questions are expecetd to be solved to a specified degree of accuracy (eg. 4 dp) using a graphics calculator or CAS technology. The source of the questions should make that clear.
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    How about some way to narrow it down to how many solutions there are?
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    Quote Originally Posted by StarKid View Post
    How about some way to narrow it down to how many solutions there are?
    Does the source of the question suggest using a calculator?
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    Quote Originally Posted by mr fantastic View Post
    Does the source of the question suggest using a calculator?
    No. It's a standardized test; I can't use anything but my brain.
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  6. #6
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    Quote Originally Posted by StarKid View Post
    No. It's a standardized test; I can't use anything but my brain.
    Tough break.

    For number of solutions, I suggest drawing sketch graphs of y = x^12 and y = 2^x and counting the number of intersection points. Ditto for the others.
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