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

Jul 26, 2015

#### Explanation:

You have:
$y = {0.3}^{x}$
that can be written as:
$y = {\left(\frac{3}{10}\right)}^{x}$ in this way you can see that
1] When $x < 0$ the value of your function gets smaller and smaller for $x \to 0$; consider for example:
$x = - 2$ then $y = {\left(\frac{3}{10}\right)}^{-} 2 = {\left(\frac{10}{3}\right)}^{2} = 11.1$
$x = - 1$ then $y = {\left(\frac{3}{10}\right)}^{-} 1 = {\left(\frac{10}{3}\right)}^{1} = 3.3$
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]}