You are looking for several things when determining if a function is exponential or not.
An exponential function needs three things. A base, a power which is always a variable, and a constant.
Let me write a random exponential function and I’ll use it as an example.
f(x)=100x1.05^x
This is an exponential function because the c (constant) is 100. The c usually is about a population or object that is increasing.
The base is 1.05 which is usually a percentage increase.
Then the power which is x and this controls the time. It could be per day, year, and etc.
All of these factors contribute to the exponential function. If you have any questions ask, don’t be shy. :)