Question

How do you determine if the equation `y = (0.3)^x` represents exponential growth or decay?

Answer 1

Exponential decay.

Explanation:

You have:
`y=0.3^x`
that can be written as:
`y=(3/10)^x` in this way you can see that
1] When `x<0` the value of your function gets smaller and smaller for `x->0`; consider for example:
`x=-2` then `y=(3/10)^-2=(10/3)^2=11.1`
`x=-1` then `y=(3/10)^-1=(10/3)^1=3.3`
2] the denominator, `10`, is always bigger (when `x>0`) than the numerator reducing the value of your fraction every time you increase the value of `x` of the exponent.
Graphically:
graph{(0.3)^x [-12.66, 12.65, -6.33, 6.33]}