Recall that exponential growth happens when a quantity increases by the same factor over equal intervals of time, and exponential decay happens when it decreases by the same factor over equal intervals of time instead.
Example function: f(x) = 2(1)^x Explanation: See solution.
Practice makes perfect
First, recall that exponential growth happens when a quantity increases by the same factor over equal intervals of time, and exponential decay when it decreases by the same factor over equal intervals of time instead. Let's consider the general form of an exponential function.
f(x)= ab^xNotice that if a>0, the function will be increasing over time by the same factor only if b>1. And, it will be decreasing over time by the same factor if 0
As we can see, the graph of this function is a horizontal line, not increasing or decreasing as we mentioned above. However, notice that this is just an example, as any function of the form f(x)= a(1)^x would satisfy the exercise's conditions. Therefore, there are infinitely many solutions.
