# What does exponential growth really mean?

1. Jul 11, 2015

### jaydnul

I've always thought that when people say exponential growth, they mean $e^x$.

But other times I hear people just say that the quantity doubles $2^x$ every time.

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

Thanks

2. Jul 11, 2015

### 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.

3. Jul 11, 2015

### DrGreg

Exponential growth means $e^{kx}$ for any constant $k$. But$$a^x = e^{x \log_e a}$$so $a^x$ is also exponential growth for any constant $a$.

4. Jul 11, 2015

### 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#