With exponential growth you have to multiply by the same number every unit of time. This number is called the growth rate for that time unit. It is always the case that $g>0$.

The general formula for exponential growth is: $H=b\cdot {\mathrm{g}}^t$.
Here $H$ is the amount and $t$ time.

Time $t$ can be any real number, even a rational and/or negative number.
And that is why all graphs for exponential growth are smooth curves.

Also, you can re-calculate the growth rate `g` per time unit to a growth rate per (for example) half the time unit or one quarter of the time unit.

• The growth rate per $\frac{1}{2}$ time unit is $g^{\frac{1}{2}}$.

• The growth rate per $\frac{1}{4}$ time unit is $g^{\frac{1}{4}}$.

Etcetera...