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Math Help - How do I manually calculate e^x?

  1. #1
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    How do I manually calculate e^x?

    Okay so I've been calculating using the simple e^x derivations. I found that on my Texas TI-89 Titanium I can use the nDeriv( command to EXTREMLY easy and fast calculate pretty much any derivation as long as I have something to go at.

    So how would you guys/girls calculate this;

    I`(7) if
    I(x) = 15'000*e^(0.24x)

    Is is possible to do this without "cheating" using my calc?
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  2. #2
    GAMMA Mathematics
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    Quote Originally Posted by Hanga View Post

    I`(7) if
    I(x) = 15'000*e^(0.24x)

    Is is possible to do this without "cheating" using my calc?
    Do you know to derive an exponential function using the chain rule? If not, then some of the lessons found here may help you.
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  3. #3
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    Quote Originally Posted by colby2152 View Post
    Do you know to derive an exponential function using the chain rule? If not, then some of the lessons found here may help you.
    I'm from Sweden so I don't know your english technical terms for math

    Anyways I pretty much do know how to derivate it;

    f(x) 15'000e^(0,24x)
    f(x) = 3600e^(0,24x)
    f(7) = 3600e^(0,24*7)

    and so on
    Still.. I can't calculate this without using my calc. How would you do it?
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  4. #4
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    Quote Originally Posted by Hanga View Post
    I'm from Sweden so I don't know your english technical terms for math

    Anyways I pretty much do know how to derivate it;

    f(x) 15'000e^(0,24x)
    f(x) = 3600e^(0,24x)
    f(7) = 3600e^(0,24*7)

    and so on
    Still.. I can't calculate this without using my calc. How would you do it?
    You have to use the calculator... Or at least use what the calculator uses
    I mean use the power series definition to get it up to required accuracy.You know e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + ..., right?
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  5. #5
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    Quote Originally Posted by Isomorphism View Post
    You have to use the calculator... Or at least use what the calculator uses
    I mean use the power series definition to get it up to required accuracy.You know e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + ..., right?
    Hehe im not in that grade of math just yet
    Still, using my calculator to do my original math problem is not really wrong then?
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  6. #6
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    Quote Originally Posted by Hanga View Post
    Hehe im not in that grade of math just yet
    Still, using my calculator to do my original math problem is not really wrong then?
    What definition of the exponential function or "e" do you have, and what do you know about it.?

    RonL
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  7. #7
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    Quote Originally Posted by CaptainBlack View Post
    What definition of the exponential function or "e" do you have, and what do you know about it.?

    RonL
    Okay so using my original quesion
    what is f(7) if

    f(x)=15'000e^(0,24x)

    The answer will be 19316 which is close to 19300.
    What I do know about e is that it's used to provide a simple derivation to
    y = a^x
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  8. #8
    GAMMA Mathematics
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    Quote Originally Posted by Hanga View Post
    What I do know about e is that it's used to provide a simple derivation to
    y = a^x
    That's not true... I wrote some notes on exponentials that should be very helpful.

    The power series that Iso provided is about the only way you could calculate such values without the use of a calculator, unless you can do such arithmetic in your head which is possible if your estimate the value of e to be about 2.7.
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  9. #9
    Grand Panjandrum
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    Quote Originally Posted by Hanga View Post
    Okay so using my original quesion
    what is f(7) if

    f(x)=15'000e^(0,24x)

    The answer will be 19316 which is close to 19300.
    What I do know about e is that it's used to provide a simple derivation to
    y = a^x
    Then there is something wrong with the course you are pursuing, you are using things that as far as you are concerned can be little different from magic.

    RonL
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  10. #10
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Hanga View Post
    Okay so using my original quesion
    what is f(7) if

    f(x)=15'000e^(0,24x)

    The answer will be 19316 which is close to 19300.
    What I do know about e is that it's used to provide a simple derivation to
    y = a^x
    If you are saying that you can use e to find {D[a^{x}]}{dx+ln(a)a^{x} I suppose you say this extremely loosely considering their is a ln(a) in the derivative which is the inverse function of x??

    and you could also graph it to approximate it if you dont want to use a power series
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  11. #11
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    What he might be referring to in the "simple derivation" for y = a^x could be that the derivative of a^x is (\ln{a})a^x and you can't find the natural logarithm without e. Or I could be wrong.
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  12. #12
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by icemanfan View Post
    What he might be referring to in the "simple derivation" for y = a^x could be that the derivative of a^x is (\ln{a})a^x and you can't find the natural logarithm without e. Or I could be wrong.
    Yeah that is what I said in the post directly above yours
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