The statement is a little misleading. He's not saying you can't have a function that grows faster than e^x as you certainly can, for example the the gamma function.
I think he's saying that for a process where the rate of growth depends on the current "population" such as interest in a bank or splitting bacteria then exponential growth is limit.
Comments
e is like a speed limit (like c, the speed of light) saying how fast you can possibly grow using a continuous process.
Can someone explain what he means? Doesn't that assume dx/dt <= x?
The statement is a little misleading. He's not saying you can't have a function that grows faster than e^x as you certainly can, for example the the gamma function.
I think he's saying that for a process where the rate of growth depends on the current "population" such as interest in a bank or splitting bacteria then exponential growth is limit.