You have just conducted a growth accounting exercise for an economy with the per capita production function latex: y_t = a_t k_{t}^{1/3} \bigg(\frac{l_{yt}}{l_t}\bigg)^{2/3 }y t = a t k t 1 / 3 ( l y t l t ) 2 / 3, where latex: k_t = \tfrac{k_t}{l_t}k t = k t l t. your results show that during the period 2002-2007 the growth rate of gdp per capita was 5%, the growth rate of the stock of ideas was 4% and both the labor force and the number of production workers were growing at 3%. at what rate did the total capital stock grow over the same time horizon?