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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.
a. Use a proportion to estimate the turtle population for 2009.
b. Use a proportion to estimate the turtle population for 2010.
a. Let x be the estimated turtle population in 2009. We can set up a proportion:
tagged turtles in 2009 / total turtles in 2009 = tagged turtles in 2008 / total turtles in 2008
Substituting the given values, we get:
16 / 50 = 40 / x
Solving for x, we cross-multiply and get:
16x = 50 * 40
x = 1,250
Therefore, the estimated turtle population in 2009 is 1,250.
b. Let y be the estimated turtle population in 2010. Using the same proportion formula, we get:
8 / 30 = 40 / y
Solving for y, we cross-multiply and get:
8y = 30 * 40
y = 120
Therefore, the estimated turtle population in 2010 is 120.