Nakano and Ikeda have proposed a novel indicator called "K" to represent a growth status in COVID-19 spread. We analyzed the mathematical properties of the K indicator with their temporal change model, and proved that the model is essentially identical to the Gompertz curve. Nakano and Ikeda derived, by fitting the data, an empirical equation k = 1+2.88K', which binds the internal model parameter k with the time derivative (K') of the K indicator. Here we derive the same equation analytically.