The population of a certain bird species at any time t (in years), for a certain area, can be modeled by the function: P(t)=500+250x/10+0.5x. What was the initial population for this species in this area? In how many years will the population exceed to 320 birds? According to this model, what is the largest number of birds of this species, that can inhabit this area? Explain your reasoning as to how you found your solution.