Answer:
Option C is correct.
[tex]f(x) = 2(\frac{1}{6})^x[/tex]
Step-by-step explanation:
Exponential function is given by:
[tex]f(x) = ab^x[/tex] where a is the initial value and b is the growth factor.
- If b >1 , then the function is exponential growth function.
- if 0<b<1 , then the function is exponential decay function.
Vertically Stretch:
A function f(x) = kg(x)
- if |k|<1, then the function is vertically compression
- if |k|> 1, then the function is vertically stretch.
From the given options only option C is correct, i.,e [tex]f(x) = 2(\frac{1}{6})^x[/tex]
As
[tex]b = \frac{1}{6} < 1[/tex]
[tex]|k| = 2 > 1[/tex]
⇒the function [tex]f(x) = 2(\frac{1}{6})^x[/tex] could be stretch of the exponential decay function.
