Is the following growth or decay f(x)=3(0.4)^x

We have the function  and we want to know if the function is growing or decaying.
The first thing we need to do is convert the decimal into a fraction. To do this we are going to add the denominator 1 to the decimal, and then we'll multiply both numerator and denominator by a power of 10 for every number after the decimal point:

Now we can rewrite our function:

Lets replace  with some integers to see how our function behaves; keep in mind that to raise a fraction to an exponent, we just raise both the numerator and denominator to the exponent:
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Notice that the denominator is growing more faster than the denominator; therefore the function is decaying.