Suppose that the (time) rate of change fish in a certain lake is proportional to the square root of the population.

(a) Find a formula P(t) for the population after t months in terms of the constant of proportionality and the initial population.

(b) Find the formula for P(t) if initially there are 100 fish and there are 169 fish after 6 months, then find how many fish will be in the lake after 1 year.