*Please show your workingstep by step.

Given the production function Y = AK^1/3L^2/3. Output per person is 170 in an economy in which 15 percent of the population are engaged in research and development, where their productivity is 0.002, and the total population size is 100 million. If this economy is on a balanced growth path, then output per personin the next periodwill be ________?

This question is in the context of endogenous growth theory and the Romer Model.