the first example that comes to me is the compound interest, as I work in banking,
from Investopedia
Compound interest = total amount of principal and interest in future (or future value) less principal amount at present (or present value)
= [P (1 + i)n] – P
another example of an exponential function is, usually, the growth and/ or decline of a city population,
in biology, the growth or decay of a bacteria.
the spread of the Corona virus is also an exponential function.
the pyramid schemes, that some people use to obtain illicit income, is an exponential function, they promise an exponential welth, like, you give me a 100, i give you back 400