Aleksandra started studying how the number of branches in her tree grows over time. Every 1.5 years, the number of branches increases by an addition of 2/7 of the total number of branches. The number of branches be modeled by a function, N, which depends on the amount of time, t (in years).

when aleksandra began the study, her tree had 52 branches.

Write a function that models the number of branches t years since aleksandra began studying her tree.

Consider the linear model for a two-stage nested design with b nested in a as given below. yijk=\small \mu + \small \taui + \small \betaj(i) + \small \varepsilon(ij)k , for i=1,; j= ; k=1, assumption: \small \varepsilon(ij)k ~ iid n (0, \small \sigma2) ; \small \taui ~ iid n(0, \small \sigmat2 ); \tiny \sum_{j=1}^{b} \small \betaj(i) =0; \small \varepsilon(ij)k and \small \taui are independent. using only the given information, derive the least square estimator of \small \betaj(i) using the appropriate constraints (sum to zero constraints) and derive e(msb(a) ).