Question

Determine if y=(1/5)^x is growth or decay

Answer 1

The function $f(x)=\left(\frac{1}{5}\right)^{x}$ is decaying.

Step-by-step explanation:

Given:

       $f(x)=\left(\frac{1}{5}\right)^{x}$

The above equation can also write as below,

    $f(x)=\frac{1}{5^{x}}$

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 ,

         $f(1)=\frac{1}{5}=0.2$

When x = 2,

      $f(2)=\frac{1}{5^{2}}=\frac{1}{25}=0.04$

When x = 3,

      $f(3)=\frac{1}{5^{3}}=0.008$

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