A Hippogriff is a magical beast that had the front legs, wings, and head of a giant eagle and the body, hind legs and tail of a horse. It is very similar to another magical creature, the Griffin, with the horse rear replacing the lion rear. A slightly different breed of Hippogriffs, living in the Rathlin Island—the northernmost point in Northern Ireland, was known to have a growth rate of 0.2 individuals per individual—year. From an initial population of N0, it grew to 35 individuals after 5 years. After 17 more years, the total population of hippogriffs in Rathlin Island rose to 1588 individuals. Solve for the carrying capacity of Rathlin Island and the initial population of the said specie.

A Hippogriff is a magical beast that had the front legs, wings, and head of a giant eagle and the body, hind legs and tail of a horse. It is very similar to another magical creature, the Griffin, with the horse rear replacing the lion rear. A slightly different breed of Hippogriffs, living in the Rathlin Island—the northernmost point in Northern Ireland, was known to have a growth rate of 0.2 individuals per individual—year. From an initial population of N0, it grew to 35 individuals after 5 years. After 17 more years, the total population of hippogriffs in Rathlin Island rose to 1588 individuals. Solve for the carrying capacity of Rathlin Island and the initial population of the said specie.