# How do you graph and determine if y=(4/3)^x is a growth or decay?

Aug 14, 2018

Growth

#### Explanation:

An exponential function has form
$y = A {r}^{x}$
where $A$ is a scaling factor and $r$ is the ratio. Here, $A = 1 \mathmr{and} r = \frac{4}{3}$. If $r > 1$, this is a growth (such as in this instance).

We can graph them by using the y-intercept and the value at $x = 1$, which are clearly $A$ and $A r$ respectively. From there, we know what an exponential growth resembles: approaches zero as $x \rightarrow - \infty$ and approaches $\infty$ as $x \rightarrow \infty$. This yields the following plot:

graph{(4/3)^x [-5, 6, -1, 5]}