Answer:
g(x) is an exponential decay function.
Step-by-step explanation:
Given : Function [tex]g(x)=(\frac{3}{4})^x[/tex]
To find : Identify the exponential function and classify the functions as indicating exponential growth or decay ?
Solution :
An exponential function is a nonlinear function of the form [tex]y = ab^x[/tex], where a ≠ 0, b ≠ 1, and b > 0.
1) When a > 0 and b > 1, the function is an exponential growth function.
2) When a > 0 and 0 < b < 1, the function is an exponential decay function.
On comparing with general function,
The given function [tex]g(x)=(\frac{3}{4})^x[/tex] is an exponential function.
Where, a=1 and [tex]b=\frac{3}{4}[/tex]
Here, [tex]b=\frac{3}{4}=0.75[/tex]
i.e. 0<0.75<1 means function is a decay function.
