Answer:
Exponential functions: [tex]f(x)=8e^x[/tex],[tex]f(x)=e^{-3x}[/tex] and [tex]f(x)=20^{\frac{x}{3}}[/tex]
Non-exponential functions: [tex]f(x)=5x^{\frac{3}{7}}[/tex], [tex]f(x)=4x^3-6x[/tex] and [tex]f(x)=\sqrt{x}+3x[/tex]
Step-by-step explanation:
The general form of an exponential function is
[tex]f(x)=ab^x[/tex]
where, a is initial value and b is growth factor.
It means the variable term i.e., x must be the exponent . In other words we can say that the variable term must be in the power of constant terms.
We need to check whether the given function is an exponential function or not.
The given function is
[tex]f(x)=8e^x[/tex]
It is an exponential function with initial value 8 and growth factor eā2.718.
Similarly,
[tex]f(x)=e^{-3x}[/tex] and [tex]f(x)=20^{\frac{x}{3}}[/tex] are exponential functions.
[tex]f(x)=5x^{\frac{3}{7}}[/tex], [tex]f(x)=4x^3-6x[/tex] and [tex]f(x)=\sqrt{x}+3x[/tex] are non-exponential functions.
