Answer:
Option: D is the correct answer.
D) [tex]f(x)=4\cdot (\dfrac{2}{3})^x[/tex]
Step-by-step explanation:
We know that a exponential function is in general represented by:
[tex]f(x)=ab^x[/tex]
where a>0 and b is called the base of the function and x is the exponent.
and if b>1 then the function is a exponential growth function
and 0<b<1 then the function is a exponential decay function.
A)
[tex]f(x)=\dfrac{1}{2}\cdot (\dfrac{3}{2})^x[/tex]
This is a exponential growth function.
Since,
[tex]b=\dfrac{3}{2}>1[/tex]
B)
[tex]f(x)=\dfrac{1}{2}\cdot (\dfrac{-3}{2})^x[/tex]
This is not a exponential function because b is not strictly greater than zero.
C)
[tex]f(x)=4\cdot (\dfrac{-2}{3})^x[/tex]
This is also not a exponential function because b is not strictly greater than zero.
D)
[tex]f(x)=4\cdot (\dfrac{2}{3})^x[/tex]
This is a exponential decay function.
Because it fulfills the condition of the exponential decay function.
Since,
[tex]b=\dfrac{2}{3}<1[/tex]
