What is the same for all exponential equations of the form $\displaystyle y=B^x $ if:
1. The value of B is greater then 1
2. The value of B is greater then 0 and less then one
First off, I assume we're talking non-negative values of X, since you can't raise, say, -2 to the power of -0.5.
That said, since the derivative would be B * [X^(B-1)], which is an increasing function for B > 0 and non-negative X's, could the answer be that what they have in common is a positive slope?
- Steve J