What does exponential growth really mean?

[jaydnul]

I've always thought that when people say exponential growth, they mean [itex]e^x[/itex].

But other times I hear people just say that the quantity doubles [itex]2^x[/itex] every time.

So which is it? And if it's just doubling, why don't we say that [itex]3^x[/itex] or [itex]4^x[/itex] is exponential growth as well, since that's what those functions are technically called?

Thanks

 

[Dr. Courtney]

Any number raised to a positive variable power is exponential growth. The rules of logs and exponents can be used to convert one equation A^x to any other equivalent aB^x.

Exponential growth means the rate of growth of a quantity is proportional to the amount currently present.

 

[DrGreg]

Exponential growth means [itex]e^{kx}[/itex] for any constant [itex]k[/itex]. But[tex]
a^x = e^{x \log_e a}
[/tex]so [itex]a^x[/itex] is also exponential growth for any constant [itex]a[/itex].

 

[Khashishi]

Another (identical) way to define exponential growth is a growth rate proportional to the current value. The classic example is population.
#dp/dt = rp#