# Is the function #f(x) = (1/5)^x# increasing or decreasing?

##### 2 Answers

#### Explanation:

Let's think about this, the function is:

so a fraction is being raised to a power, what does that mean?

but 1 to any power is just 1 so:

so as x gets bigger and bigger the number dividing 1 gets huge and the value gets closer and closer to 0.

So

graph{ (1/5)^x [-28.87, 28.87, -14.43, 14.44]}

Decreasing

#### Explanation:

graph{(1/5)^x [-20, 20, -10.42, 10.42]}

In graphs of the form

As exponential decay is measured as when a population or group of something is declining, and the amount that decreases is proportional to the size of the population, we can clearly see that happening in the equation of **decrease** in the positive direction of the **increase** in the positive direction of the

I hope I helped!