Respuesta :

The function [tex]f(x)=\left(\frac{1}{5}\right)^{x}[/tex] is decaying.

Step-by-step explanation:

Given:

       [tex]f(x)=\left(\frac{1}{5}\right)^{x}[/tex]

The above equation can also write as below,

    [tex]f(x)=\frac{1}{5^{x}}[/tex]

Now from the function we can see that as we are increasing the value of x the value of function is decreasing.  Let take some values of x and then find out the value of function at those value of x

When x = 1 ,

         [tex]f(1)=\frac{1}{5}=0.2[/tex]

When x = 2,

      [tex]f(2)=\frac{1}{5^{2}}=\frac{1}{25}=0.04[/tex]

When x = 3,

      [tex]f(3)=\frac{1}{5^{3}}=0.008[/tex]

So, from the above examples, we can see that the value of function is decreasing on increasing the value of x. Hence the function is decay

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