# How do you determine whether each function represents exponential growth or decay #y=0.4(1/3)^x#?

##### 2 Answers

it's decay. see explanation

#### Explanation:

Exponential function:

Formula:

where:

-a is multyplier of

-c moves function on y axis

-b is a base of exponential function. b must be greater than 0 and can't be 1 (everything on the first is equal one, so it makes no sense thinking about it as exponential function)

if b>1 then it is growing; if

Given:

a=0.4;

graph{y=0.4(1/3)^x [-10, 10, -5, 5]}

#### Explanation:

This is an interesting problem, but one way that you can determine weather a function is undergoing exponential decay or growth, is by considering its behavour as

So lets consider your function:

As

But we can generalise this a bit further:

If we have

If

If

If

So for example:

Hence this function undergoes exponential decay...