4 ms·
The very meaning of an exponential function is that any point t plus a fixed delta t the value is higher than the value at t by a constant factor. If that facto
by stkdump 7y ago
The very meaning of an exponential function is that any point t plus a fixed delta t the value is higher than the value at t by a constant factor. If that factor is getting lower over time it is not exponential anymore, even when it stays above 1. Otherwise you could argue that a quadratic function is exponential as well.
- rat9988 7y agoThis is not the meaning of an exponential function but merely a property of exponential function with a base > 1.
- stkdump 7y agoTell me another function for which this property holds, but that isn't exponential.
- rat9988 7y agoPolynomial as you stated.
- stkdump 7y agoNo, a polynomial does not have a constant factor for every t.
- rat9988 7y agoI may have misunderstood your assertion then. Did you mean the following? Did you mean something like, here exists some delta and t as for every x>y, with y an element of R, f(x+t) > f(x)+delta
- stkdump 7y agoYou can choose any delta, so that f(t)*constant=f(t+delta) for every t.
- rat9988 7y agoI have misunderstood your original comment. You are indeed correct. Edit: I just noticed that the function which maps x to 0 satisfies this condition as well, but isn't the exponential function if we consider 0 as part of the domain definition. It doesn't matter much for our discussion though.