The exponential learning equation as a function of successful trials results in sigmoid performance

While the exponential learning equation, indicating a gradually diminishing improvement, is one of the standard equations to describe learning, a sigmoid behavior with initially increasing then decreasing improvement has also been suggested. Here we show that the sigmoid behavior is mathematically derived from the standard exponential equation when the independent variable of the equation is restricted to the successful trials alone. It is suggested that for tasks promoting success-based learning, performance is better described by the derived sigmoid curve.