Based on analysis of the variation of ²¹⁰Pb_ex inventory in soil of cultivated land in response to changes in soil erosion rate, mistakes in calculation of soil erosion rate of cultivated land using the ²¹⁰Pb_ex method are discussed. A model is established to fit response of ²¹⁰Pb_ex inventory to variation of soil erosion rate in soil of cultivated land, based on the principle of mass balance, demonstrating that the long-commonly-held assumption that what is determined with the ¹³⁷Cs method is the mean soil erosion rate of the past 40 a or 50 a and with the ²¹⁰Pb_ex method the mean of a longer past of 100 a or 200 a is incorrect. The model is used to fit response of ²¹⁰Pb_ex inventory to the variation of soil erosion rate from 0.06 cm a^-1 to 0.6 cm a^-1 and from 0.6 cm a^-1 to 0.06 cm a^-1. The results indicate that ²¹⁰Pb_ex inventory responds quickly, which rises or reduce exponentially with time, but negatively with soil erosion rate. Consequently, ²¹⁰Pb_ex can replace ¹³⁷Cs in determining soil erosion rate in cultivated land not only 100 years old, but also just a few years old due to change in land use.