The value of the base determines whether the graph of an exponential function is increasing or decreasing from left to right.
How an exponential function is represented?
- The exponential function is represented by [tex]f(x)=b^x[/tex] and its graph is represented by [tex]y=b^x[/tex].
- Here x is the independent variable and y is the dependent variable.
- Here b is the base of the function and x is the exponent.
- The exponential growth or decay depends on base b.
How do exponential growth and decay depend on base value?
The exponential growth or decay depends on the base value of the function.
If the base value b > 1, the graph grows exponentially as the value of x increases.
If the base value is in between 0 < b < 1, then the graph decays exponentially as the value of x increases.
These are expressed in the graphs below.
So, the base value determines the graph of the exponential function.
Learn more about the graph of the exponential function here:
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