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

2 Answers
May 24, 2018

f(x) is decreasing..

Explanation:

Let's think about this, the function is:

f(x) = (1/5)^x

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

(1/5)^x = (1^x)/(5^x)

but 1 to any power is just 1 so:

(1/5)^x = (1^x)/(5^x) = (1)/(5^x)

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

f(1) = 1/5 = 0.2

f(2) = 1/25 = 0.04

f(3) = 1/125 = 0.008

So f(x) is decreasing closer and closer to 0.

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

May 24, 2018

Decreasing

Explanation:

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

In graphs of the form f(x)=a^x where 0 < a<1, as x increases, y decreases, and vice-versa.

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 f(x)=(1/5)^x. Also keep in mind that exponential decay relates to a proportional decrease in the positive direction of the x-axis, while exponential growth relates to a proportional increase in the positive direction of the x-axis, so just from looking at the graph the answer can be clearly seen.

I hope I helped!