So far we have observed that exponential fucntions have very similar form and shape and vary only in steepness. We have also observed that the steepness seems to be a constant factor that increases at the base increases.
How cool would it be if we found the PERFECT function where the slope and the y-value were exactly equal! That is, the special ratio for this exponential would be 1 !
Go back to the above graph and move the black slider. Take note that the ratio is less than 1 for base = 2 but greater than one for base = 3. For all bases bigger than 3 the ratio just keeps getting bigger.
Let's take a closer look BETWEEN the base being 2 and 3 below.