The initial value is 1
The base, or rate of change is 1/3
The domain is a set of all real numbers
How to Interpret the Exponential Function Graph?
An exponential function is a function with the general form:
y = abˣ
Where:
a is the initial value ≠ 0
b is the base or rate of change which is a positive real number which is the growth or decay rate
b ≠ 1.
x is the time exponent
In an exponential function, the base b is a constant. The exponent x is the independent variable where the domain is the set of real numbers.
For the graph, we see that:
When x = 0, y = 1. Thus:
a = 1
When x = 1, y = 1/3
When x = 2, y = 1/9
Thus:
b = 1/3
Thus:
The initial value is 1
The base, or rate of change is 1/3
The domain is a set of all real numbers