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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.
Part A: Use a proportion to estimate the turtle population for 2009.
Part B: Use a a proportion to estimate the turtle population for 2010.
Part A:
Let x be the estimated turtle population for 2009.
The proportion of tagged turtles to the total captured turtles in 2009 is equal to the proportion of tagged turtles to the total turtles in the population:
16/50 = 40/x
To solve for x, we can cross-multiply and simplify:
16x = 40*50
16x = 2000
x = 2000/16
x = 125
Therefore, the estimated turtle population for 2009 is 125.
Part B:
Let y be the estimated turtle population for 2010.
The proportion of tagged turtles to the total captured turtles in 2010 is equal to the proportion of tagged turtles to the total turtles in the population:
8/30 = 40/y
To solve for y, we can cross-multiply and simplify:
8y = 40*30
8y = 1200
y = 1200/8
y = 150
Therefore, the estimated turtle population for 2010 is 150.