Exponential functions are functions of the base of natural logarithms e.
Exponential Growth shows the steep rise if the basic function f(x) = exp(x).
Exponential Decay shows the way a value decays asymptotically towards zero from a starting value. Both of these occur in almost every aspect of engineering and physics.
Catenary or hyberbolic cosine is an exponential function which describes the shape of a string or chain suspended between two supports, for example a suspension bridge.
Hyperbolic sine (sinh) is an exponential function similar to its trigonometric counterpart.