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. The limiting population is 160.

(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.The limiting population is 180.