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Math Help - Exponential Function and POint (0,1)

  1. #1
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    Exponential Function and POint (0,1)

    Do all exponential functions go through the point (0, 1)?

    If so, why is this the case?

    The math book does not share the "WHY" with its readers.

    I am just curious.

    Thanks
    Last edited by magentarita; July 29th 2008 at 06:42 AM. Reason: Need to add quotation marks
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by magentarita View Post
    Do all exponential functions go through the point (0, 1)?

    If so, why is this the case?

    The math book does not share the "WHY" with its readers.

    I am just curious.

    Thanks
    It depends on what you call an exponential function.

    f(x)=e^{ax}, where a is a constant.
    f(0)=e^{a \cdot 0}=1, so it goes through the point (0,1).

    If f(x)=be^{ax}, where a is a constant and b is a non-zero constant, then f(0)=be^{a \cdot 0}=b, so it goes through the point (0,b).
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  3. #3
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    Not Clear????

    Your reply is not too clear. This is a precalculus question and not to be answered using advanced math language.

    I just want to know why the exponential functions must go through the point (0,1).

    Is there a reason?
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  4. #4
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    Quote Originally Posted by magentarita View Post
    Your reply is not too clear. This is a precalculus question and not to be answered using advanced math language.

    I just want to know why the exponential functions must go through the point (0,1).

    Is there a reason?
    Consider a simple exponential function with the base b. b must be positive and mostly b must be unequal 1. (With your question this constraint isn't necessary)

    The equation of the function could be: y = b^x. A point of the graph of this function has the coordinates P(x, y) or in words:

    P is on the graph if the coordinates consist of (exponent, value of the power). The base is considered to be a constant.

    If the exponent is zero, the value of the power is b^0 which is by definition 1.

    And therefore the graphs of all exponential functions with the equation mentioned above will pass through the point P(1, 0)
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  5. #5
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    earboth

    Good job earboth.

    Thanks!

    What is the meaning of your username?
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  6. #6
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Moo View Post
    Hello,

    It depends on what you call an exponential function.

    f(x)=e^{ax}, where a is a constant.
    f(0)=e^{a \cdot 0}=1, so it goes through the point (0,1).

    If f(x)=be^{ax}, where a is a constant and b is a non-zero constant, then f(0)=be^{a \cdot 0}=b, so it goes through the point (0,b).
    Quote Originally Posted by magentarita View Post
    Your reply is not too clear. This is a precalculus question and not to be answered using advanced math language.

    I just want to know why the exponential functions must go through the point (0,1).

    Is there a reason?
    I don't want to sound rude, but what Moo used was not advanced math language. Someone in precalc should be able to understand what she said.

    All she said was this:

    It depends on how you define the exponential function.

    If we have an exponential function f(x)=a^x where a has a constant value, the value of the function at x=0 is f(0)=a^0=1, thus it passes through the point (0,1).

    However, if you defind an exponential function as f(x)=b\cdot a^x, where b is some number, then the value of the function at x=0 is f(0)=b\cdot a^0=b\cdot 1=b, thus it passes through the point (0,b)

    This shouldn't be that hard to grasp.

    --Chris
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  7. #7
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    Chris

    Thanks Chris for your input.
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