Over the period from a.d. 1 to a.d. 2000, the world population is estimated to have increased from 170 million to 6 billion, while the level of income per capita increased by 0.13 percent annually. Assuming that the quantities of human and physical capital per worker did not change, and that the exponent on land in the production function is one-third, calculate the total growth in productivity over this period. What was the annual growth rate of productivity, A?