The population of bats in a large cave is 4800 and is growing exponentially at 17% per year. Write a function to represent the population of bats after t years, where the
monthly rate of change can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also, determine the percentage
rate of change per month, to the nearest hundredth of a percent.

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) ).