```Question 607024

recall that an {{{exponential}}} function is called the {{{base}}}

you first look is there {{{ratio}}}...if you find one, means the function is an {{{exponential}}} function

keep this in mind:

The pattern in the table of an {{{exponential}}} function {{{resembles}}} the pattern in a {{{linear}}} function, in that it can be checked easily as long as the {{{input}}} values are {{{equally}}} spaced.

The {{{constants}}} in an {{{exponential}}} function come from {{{division}}}, as opposed to subtraction.  Recall that when the input values have difference one, then the constant difference in a {{{linear}}} function is called the {{{slope}}}.  Analogously, when the differences in the input values of an {{{exponential}}} function have difference one, then the constant {{{ratio}}} in an {{{exponential}}} function is called the {{{base}}}.

For {{{exponential}}} functions, when the {{{inputs}}} increase by a {{{constant}}}{{{ amount}}}, the {{{outputs}}} increase {{{or}}} decrease by the {{{same}}}{{{ ratio}}}.

Note that with an exponential function, if we change the spacing of the inputs, we will change the ratio, although the ratios will still be the same as each other, as long as inputs are equally spaced.

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