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

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- Dec 8th 2008, 07:26 PMeuclid2exponential equations
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 - Dec 8th 2008, 10:02 PMSteve_Jexponential equations
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 - Dec 8th 2008, 10:12 PMChop Suey
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.