At what rate does the aggregate population of workers grow?

Let us consider a Solow growth model augmented with human capital. The aggregate output/income 1': at every time tis produced according to the following production function: V: = AK?\" 0?th)\" whereA > 0, a, ,8 6 (0,1) are production parameters, Kt stands for the aggregate physical capital, ht represents the human capital per worker: ht E Ht/Lt, Ht denotes the aggregate level of human capital and L; is the aggregate number of workers. At every time t, the aggregate number of workers is assumed to be a fraction y 6 (0,1) of the aggregate population size denoted by Mr which grows at a constant rate 11 > 0: Nt+1 = (1 + \")1\": The change in the aggregate physical capital from time tto time {+1 can be written as: Kc+1 Kt = 1;; 5K: where 6 E (0.1) represents the depreciation rate and If denotes the aggregate investment in physical capital which in equilibrium is assumed to be a constant fraction 3 e(0,1) of the aggregate output/income: I? = EYt The change in the aggregate human capital from time tto time {+1 can be written as: Ht+1 H: = If 5H: where 1? denotes the aggregate investment human capital which in equilibrium is assumed to be a oonstant fraction I-I E(0,1) of the aggregate output/income: If = \"Y: At every time t, the goods' market is in equilibrium if: =q+$+ where C; denotes aggregate consumption at time t. Let yr 5 Yt/Nt denotes the income/output per capita at time t, kt E Kt/Nt stands for the physical capital per capita and or E (It/NI is for the physical capital per capita. a. At what rate does the aggregate population of workers grow? (4 points)