Question

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

Answer 1

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 and r = 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 `Ar` 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]}