Question

In exponential growth functions, the base of the exponent must be greater than one. how would the function change if the base of the exponent were 1? how would the function change if the base were between 0 and 1?- and can someone help me understand exponential growth, it's so confusing-

Answer 1

An exponential function with a base greater than 1 looks as follows:

And an exponential funcion with a base of 1 looks as follows:

So now we can answer the question:

how would the function change if the base of the exponent were 1?

When the base of the exponent is 1, the function has a fixed value of 1, and do not behave the same as when the base is greater than 1.

To answer the next question we need to know how a function with a base between 0 and 1 would look like. Let's take the following example:

And we can now answer:

how would the function change if the base were between 0 and 1?

The function looks like it is inverted (in comparison with the function with a base greater than 1). Meaning that as x increases, the values of the function decrease.