A nature reserve on an island contains a population of endangered turtles. The reserve is not fenced, so the turtles are free to cross the boundary coming in or going out. Every year, 10% of the turtles leave the reserve, while 1% of the turtles from outside the reserve (but on the island) make their way in. 1. Suppose the island has a total of 2,200 turtles. Is there a population of turtles inside and outside the reserve that will stay constant over time? 2. Suppose that the turtle population outside the reserve is growing by 1% each year. Is there an initial population of turtles that can be established inside the reserve so that it grows at the same rate as outside, every year? 3. Is there another rate of growth (aside from keeping the population constant) that can be achieved both inside and outside the reserve simultaneously? What should be the initial population of turtles inside and outside the reserve for this to happen?
A nature reserve on an island contains a population of endangered turtles. The reserve is not fenced, so the turtles are free to cross the boundary coming in or going out.
Every year, 10% of the turtles leave the reserve, while 1% of the turtles from outside the reserve (but on the
island) make their way in.
1. Suppose the island has a total of 2,200 turtles. Is there a population of turtles inside and outside the reserve that will stay constant over time?
2. Suppose that the turtle population outside the reserve is growing by 1% each year. Is there an initial population of turtles that can be established inside the reserve so that it grows at the same rate as outside, every year? 3. Is there another rate of growth (aside from keeping the population constant) that can be achieved both inside and outside the reserve simultaneously? What should be the initial population of turtles inside and outside the reserve for this to happen?
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