Question

How do you determine whether each function represents exponential growth or decay `y=(0.5)^x`?

Answer 1

As shown below:

Explanation:

For this problem we can sketch the function, what will be able to determine weather its decaying or not:

`y = 0.5^x -= 2^(-x)`:
As `x-> oo , y -> 0`
and `x->-oo , y -> oo`

graph{0.5^x [-9.08, 10.92, -2.72, 7.28]}

In general:

`y = beta^x`

If `beta > 1` the function undergoes exponential growth
if `beta < 1` the function undergoes exponential decay
if `beta = 1` it represents a straight line