Question

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

Answer 1

The function
`f(x)=\left((1)/(5)\right)^(x)` is decaying.

Explanation:

Given:

`f(x)=\left((1)/(5)\right)^(x)`

The above equation can also write as below,

`f(x)=(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)=(1)/(5)=0.2`

When x = 2,

`f(2)=(1)/(5^(2))=(1)/(25)=0.04`

When x = 3,

`f(3)=(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