There are some exponential functions that increase by a constant factor or percentage over equal intervals of time, while others decrease by a constant factor or percentage instead.
See solution.
Practice makes perfect
From what we can see in Exploration 1, we know that there are some specific groups of exponential functions that increase by a constant factor or percentage over equal intervals of x. For these cases, we say that the functions exhibit exponential growth.
Let's recall the form of an exponential function.
y = ab^x
If we consider a>0, the exponential function will be increasing over time only if b>1. Therefore, we can rewrite the exponential function as shown below.
y = ab^x ⇔ y = a(1+r)^x
Here r represents how fast the function is growing as a percentage, written in decimal form. This is why r is known as the growth rate in these cases. On the other hand, if the function is decreasing by a constant factor or percentage over equal intervals of x, we say that it exhibits exponential decay.
For this to happen, we need that 0decay rate in these cases.
