Thread: exponential equations

What is the same for all exponential equations of the form 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

Just to name a few:
- They all cross the y-axis at (0,1)
- They may never cross the x-axis.
- Their domains are sets of real numbers and ranges are sets of positive real numbers.