Which function equation for exponential function?
Hi,
I found two different types of equations for exponential functions on the Internet:
1) f(x)=b*a^(c*x+d)+e
2) f(x)=b*a^(x)
For me, the first equation makes more sense because it includes all the parameters for the displacement, but it's impossible to create such an equation using two given points. (For example, using P (0/7) would give you b=7 in the second equation, but that's not possible in the first.)
What is correct now????
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What is “right” is not a very sensible question.
Depending on the intended use, both formulas can be useful.
The first formula, however, somehow has at least one parameter “too much”, because you could also use an equation of a somewhat simpler form for each graph.
f(x)=d*a^(k*x)+e
or even
f(x) = d*b^x + e
represent.
Ahhh ok, so you can describe the same function with both equations?
Your first equation is more “rich”. But it is also something “redundant” in itself.
the first equation is the more general form
in contrast to 2) it has a displacement in the y-direction (parameter e), a yield factor in the x-direction (c) and a displacement in the x-direction (d), wherein the displacement is also dependent on c)
The function (1) is somewhat strangely “overparametrized” because and
and the application of the potency laws results in
Only one shift in the y-direction by “e” remains at the end of the entire definition (1).