Real world applications of exponential function; continous case I am looking for interesting applications in everyday life, technology or science of exponential functions of the type:
$$
f\colon \mathbb{R} \to \mathbb{R}, \quad x \mapsto ab^x
$$
for the case $a > 0$ and $b > 1$. 
I am also interested in other examples which are in some way fascinating or funny for this case.
I don't want any discrete examples or such involving the Euler number $\mathrm{e}$. 
Any suggestions for that?
 A: $a>0$ and $b>1$ correspond to exponential growths. Thius kind of formula is used in studies about population, virus, bacteria, ...But you have one case which is very common : make a deposit of $a$ dollars on your bank account and let us suppose that the bank gives you an interest of $r$% per year. After $n$ years, your initial $a$ dollars will become $a \left(1+\frac{r}{100}\right)^n$ dollars. 
Now, if your bank is generous and if you are patient, you will be rich. Suppose that you invest today $100$ dollars, that your generous bank gives you a $5$ % interest (give me its name) and that you are ready to wait for $20$ years, then, in year 2034, you will be able to cash $265$ dollars.  
Unfortunately, with bacteria and virus, this goes much faster. For example  if we start with only one bacteria which can double every hour, by the end of one day we will have almost 17 million bacteria. 
Another example is the number of cell phones. They increased just as bacteria (slightly slower but very fast).
