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July 19th, 2017, 06:52 AM   #1
EDL
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Question on exponential functions

So, I'm taking an online class for college algebra and we just started exponential and logarithmic functions.

Our instructor urges us to think about the math and not just learn formulas and to plug in numbers, sooooo I did just that and now I have a question.

In particular, if I were to take the most basic exponential function as a representation of the growth rate of computer power, say $\displaystyle y=3^x$, and plot that on a graph with x as the time line and y as the growth, that means the x axis is also the asymptote.

No matter what value I plug in for the timeline, I will always get a positive result for the power of a computer...even at a time when computers did not even exist.

So, I figure I am thinking about this equation and how it works incorrectly, or there is some other answer?
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July 19th, 2017, 03:24 PM   #2
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Quote:
Originally Posted by EDL View Post
So, I'm taking an online class for college algebra and we just started exponential and logarithmic functions.

Our instructor urges us to think about the math and not just learn formulas and to plug in numbers, sooooo I did just that and now I have a question.

In particular, if I were to take the most basic exponential function as a representation of the growth rate of computer power, say $\displaystyle y=3^x$, and plot that on a graph with x as the time line and y as the growth, that means the x axis is also the asymptote.

No matter what value I plug in for the timeline, I will always get a positive result for the power of a computer...even at a time when computers did not even exist.

So, I figure I am thinking about this equation and how it works incorrectly, or there is some other answer?
Models are models and in particular they have a range of inputs over which they produce accurate results and inputs outside of this range may well produce nonsensical results.

In the case of a model like $y=a^x$, then yes, positive results will be returned for values of $x$ that correspond to before the universe existed. This is a case of inputs being outside the valid range for this model.

Such is life. One can either strive to find a model that covers a larger range of inputs, or to deal with restricting one's inputs to the valid range of the model at hand. Only you can know which is more amenable to satisfying your needs.
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