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, we can set up a proportion:
Tagged turtles in 2009 / Total turtles captured in 2009 = Tagged turtles in 2008 / Total turtle population in 2008
Plugging in the numbers given, we get:
16 / 50 = 40 / x
where x is the estimated total turtle population in 2009. Cross-multiplying and solving for x, we get:
x = (50 x 40) / 16 = 125 turtles (rounded to nearest whole number)
Therefore, the estimated turtle population for 2009 is 125.
To estimate the turtle population for 2010, we can set up a similar proportion:
Tagged turtles in 2010 / Total turtles captured in 2010 = Tagged turtles in 2008 / Total turtle population in 2008
Plugging in the numbers given, we get:
8 / 30 = 40 / x
where x is the estimated total turtle population in 2010. Cross-multiplying and solving for x, we get:
x = (30 x 40) / 8 = 150 turtles (rounded to nearest whole number)
Therefore, the estimated turtle population for 2010 is 150.