Question

How do you determine if the equation `y = (2)^x` represents exponential growth or decay?

Answer 1

When `x>1` it represents growth, when `x<1` it represents decay.

(When `x=1` it is a constant)

Answer 2

Check the sign of the exponent, and you will find that it represents exponential growth.

Explanation:

As `x` increases in value, `y` increases as well, and will approach infinity with increasing `x`. This is because the equation is raising 2 to `+x`, indicating exponential growth (see below).

graph{2^x [-23.17, 56.83, -6.88, 33.12]}

If the equation was `y=2^(-x)` y would be in exponential decay, with `y` approaching 0 as `x` goes to infinity. Again, we can show this on a plot (see below).

graph{2^(-x) [-23.17, 56.83, -6.88, 33.12]}

Basically, the sign of the exponent tells you if the function is increasing or decreasing.