1. The proportion can be set up as follows:
tagged turtles in 2009 / total turtles captured in 2009 = tagged turtles in 2008 / total population in 2008
Simplifying this proportion, we get:
16/50 = 40/x
where x is the estimated total population in 2009. We can cross-multiply and solve for x:
16x = 2000
x = 125
Therefore, we can estimate that there were 125 giant turtles in the population in 2009.
2. The proportion for 2010 can be set up similarly:
tagged turtles in 2010 / total turtles captured in 2010 = tagged turtles in 2008 / total population in 2008
Simplifying the proportion:
8/30 = 40/x
Cross-multiplying and solving for x:
8x = 1200
x = 150
Thus, we can estimate that there were 150 giant turtles in the population in 2010.
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.
1. Use a proportion to estimate the turtle population for 2009.
2. Use a proportion to estimate the turtle population for 2010.
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