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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 use the following proportion:
(tagged turtles in 2009) / (total turtles in 2009) = (tagged turtles in 2008) / (total turtles in 2008)
Solving for total turtles in 2009:
(total turtles in 2009) = (tagged turtles in 2009) / [(tagged turtles in 2008) / (total turtles in 2008)]
(total turtles in 2009) = (16) / [(40) / (2008)]
(total turtles in 2009) = 802
Therefore, the estimated turtle population for 2009 is 802.
For 2010, we can use the same proportion:
(tagged turtles in 2010) / (total turtles in 2010) = (tagged turtles in 2008) / (total turtles in 2008)
Solving for total turtles in 2010:
(total turtles in 2010) = (tagged turtles in 2010) / [(tagged turtles in 2008) / (total turtles in 2008)]
(total turtles in 2010) = (8) / [(40) / (2008)]
(total turtles in 2010) = 402.4
Therefore, the estimated turtle population for 2010 is 402.4 (rounded to the nearest whole number, it is 402).