What is the relationship between the growth factor of an exponential and its Δy/Δx vs y?
How can I find what the growth factor of the exponential model is, from the Δy/Δx vs y equation? How do they relate to each other?
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What do you mean by "Δy/Δx"? Are you referring to the standard "dy/dx," denoting a derivative?
The Δ symbol does indicate change... as does the 'd' in Leibniz's notation of the derivative... but the 'd' refers to an infinitesimal change while Δ refers to any finite change.
Anyway... the rate of change of any exponential function y = a^x will have a value of ln(a)⋅a^x
If y = a^x then
y' = dy/dx = ln(a)⋅a^x
It is no coincidence that the transcendental number 'e', Euler's number (approx 2.718281828...) works beautifully with this.
If y = e^x
then y' = dy/dx = e^x
... the functional value and its instantaneous slopes are the same.
That is no coincidence. This is the defining basis for what 'e' is. The value for e was evaluated using the above definitions
Linear Function y=22x+22