3 ms·
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
by ced 15y ago
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?
- parallel 15y agoThe 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.
- deleted 15y ago[deleted]
- kalid 15y agoyes, i need to clarify. basically, if you have a button which lets your earned interest start working for you (or your bacteria maturing and beginning to divide on their own) then e is the idea of holding down the button. new money starts earning money the instant it is made (banks do not do this and add in your earned interest, ie push the button, daily or monthly). the speed limit is on how long you wait to add in your growth (e is the minimum possible), not the absolute rate itself. i should add this to the article.