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.

1 answer

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.