Exponential Functions: Graphing (page 3 of 5) Sections: Introduction, Evaluation, Graphing, Compound interest, The natural exponential
So y = (^{ 1}/_{3} )^{–x} does indeed model growth. For the record, however, the base for exponential functions is usually greater than 1, so growth is usually in the form "3^{x}" (that is, with a "positive" exponent) and decay is usually in the form "3^{–x}" (that is, with a "negative" exponent). Every once in a while they'll give you a morecomplicated exponential function to deal with:
Note that, for graphing, the decimal approximations are more useful than the "exact" forms. For instance, it is hard to know where "e^{2.25}" should be plotted, but it's easy to find where "9.488" goes. Note also that I calculated more than just wholenumber points. The exponential function grows way too fast for me to use a wide range of xvalues (I mean, look how big y got when x was only 2). Instead, I had to pick some inbetween points in order to have enough reasonable dots for my graph.
The above function did involve an exponential, but was not in the "usual" exponential form (since the power was not linear, but quadratic). However, usually you'll get the morestandard form, with a greaterthanone base, perhaps multiplied by some constant, and a linear exponent. Note that the graphs all look roughly the same; they may have been moved up or down, flipped upsidedown, shifted left or right, etc, etc, but they all pretty much have the same shape:



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