Enter your answer and show all the steps that you use to solve this problem in the space provided. A researcher tagged 40 giant turtles in 2008. In 2009, she returned and captured 50 turtles, 16 of which were tagged. In 2010, she returned again and captured 30 turtles, 8 of which were tagged. Use a proportion to estimate the turtle population for 2009. Use a proportion to estimate the turtle population for 2010.
To estimate the turtle population for 2009 using a proportion, we can set up the following equation:
tagged turtles in 2009 / total number of turtles in 2009 = tagged turtles in 2008 / total number of turtles in 2008
Plugging in the given values, we get:
16 / 50 = x / 40
Simplifying this equation, we can cross-multiply to get:
16 * 40 = 50 * x
Dividing both sides by 50, we get:
x = 12.8
Therefore, we can estimate that the turtle population in 2009 was approximately 12.8 * 50 = 640.
To estimate the turtle population for 2010 using a proportion, we can set up the equation:
tagged turtles in 2010 / total number of turtles in 2010 = tagged turtles in 2008 / total number of turtles in 2008
Plugging in the given values, we get:
8 / 30 = x / 40
Simplifying this equation, we can cross-multiply to get:
8 * 40 = 30 * x
Dividing both sides by 30, we get:
x = 10.67
Therefore, we can estimate that the turtle population in 2010 was approximately 10.67 * 30 = 320.