Question

In exponential growth functions, the base of the exponent must be greater than 1. How would the function change if the base of the exponent were 1? How would the function change if the base of the exponent were between 0 and 1?

Answer 1

First, let's start with 1:
1^1 = 1
1^2 = 1
1^3 = 1
1^x = 1
It would be quite boring if we used 1

When the base is greater than 1, the function speeds up quickly and zips towards infinity. When the base is less than 1, it gets closer and closer to zero but never reaches it.

If you know what the graph looks like for an exponential graph, imagine you flip it sideways; now you have a backward "J" where the base is less than 1.

Hope this helps!

Answer 2

Explanation:

In exponential growth functions, the base of the exponent must be greater than 1.

If base =1 since 1 to power of any natural number is 1, there is no exponential growth or decay.

This becomes a constant function.

If base lies between 0 and 1 we have for values between 0 and 1 raised to powers 2 or 3 will reduce its value. i.e. there is exponential decay when base of the exponent lies between 0 and 1.