The situation where a quantity is multiplied by a certain number every time step is called exponential growth. This number `g` is called the growth rate and corresponds to the unit of time: `g>0` .
To determine whether a quantity $H$ grows exponentially, you compute the ratio of consecutive values. If these ratios are (approximately) equal, you are dealing with exponential growth. The quantity $H$ then grows like this:

• At $t=0$ the initial value is $b$.

• At $t=1$ you have $H=b\cdot g$.

• At $t=2$ you have $H=b\cdot g\cdot g=b\cdot g^2$.

• At $t=3$ you have $H=b\cdot g\cdot g\cdot g=b\cdot g^3$.

So the formula $H=b\cdot g^{\mathrm{t}}$ applies .

When working with exponential growth you use powers: when you multiply the same number `g` $t$ times, you write $g^{\mathrm{t}}$. This is a power, where the growth rate $g$ is called the base and $t$ is called the exponent.

An example of exponential growth is growth or decay with a fixed percentage. When the growth is $p$ percent, the growth rate is: $g=1+\frac{p}{100}$. When $p>0$ the quantity increases and `g>1` : exponential growth. When $p<0$ the quantity decreases and `g < 1` (but greater than 0): exponential decay.