> I am writing notes to teach a unit comparing linear functions to
> exponential functions. I have defined the growth rate for a linear
> function to be either the change in y when x changes by one unit or the
> change in y divided by the change in x. With a linear function the
> growth rate is a constant which can be seen in a linear equation as the
> slope.
>
> My question is about vocabulary for the corresponding characteristic
> with exponential functions. For
> y = 3(1.2)^x I would say that there is a "growth factor" of 1.2,
> meaning that when x increases by 1 then the value of y is
> correspondingly multiplied by 1.2 (thereby making sense of using the
> word "factor" in the terminology)
>
> Using a table of values, the growth factor is the ratio of new value
> of y divided by original value of y when x changes by one. Is this use
> of the term "growth factor" common and acceptable? ( I have seen the
> idea of saying there is a 20% growth rate, but want to avoid that
> terminologyl. I feel it would be confusing now that I have used growth
> rate as I have for the linear functions.)
>
> My purpose is to contrast "growth rate" for linear functions with
> "growth factor" for exponential functions. Any opinions?
> This is a pre-calculus class.
I would call this an excellent approach to furthering the understanding of what
an exponential function is (and does). The whole point is that linear
functions are _additive_ and (simple) exponential functions are
_multiplicative_, but otherwise have much in common. This should also help
open the door to the concept of logarithm, when you get to it.
RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623
>>>> The plural of mongoose begins with p. <<<<
P.S. The concept corresponding to _slope_ is actually _base_, isn't it?
Or would it be the _log_ of the base?
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