What is a function that increases proportionally to it's current value?

A function that increases proportionally to its current value is an exponential function, typically expressed as ( f(x) = ae^{bx} ), where ( a ) is a constant, ( b ) is a positive constant, and ( e ) is the base of the natural logarithm. In this case, the rate of growth at any point is directly proportional to the function's current value. This characteristic is commonly seen in processes such as population growth and compound interest.