please answer with calculations, thanks a lot

Consider the human capital growth model with the representative consumer. The efciency pa- rameter of human capital accumulation technology is b. The total productivity factor is given by z = 1. Denote by Ht the human capital accumulated in period t, and by u the time Spent working in period t. Assume the initial human capital is H0 = 1. 1. Compute the consumer consumption 0,: for periods 0 and 1 as a function of a. ([02.00 pts]) Assume there are only two periods and the consumer is willing to maximize his utility func- tion, 1n(01) 1 + r ' F(u)=00+ where 1" = 0.1 is the real interest rate. . Find the optlmal value of u. ([08 pts]) . Empirically, it has been observed that the annual growth rate of the country consumption per capita has been close to 2.5% historically. Taking this as granted, what is your estimate of b? ([03 pts]) After how many years will the consumption double? ([03 pts]) . Quantity the implication of a 10% increase in 2 on the long term consumption growth rate. ([04 ptSD