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.

Question

Use a proportion to estimate the turtle population for 2009.
Use a proportion to estimate the turtle population for 2010..

Answer 1

For 2009:

Let x be the turtle population for 2009.
The proportion can be set up as:

tagged turtles in 2009 / total number of turtles in 2009 = tagged turtles in 2008 / total number of turtles in 2008

Plugging in the known values, we get:

16 / 50 = 40 / x

Cross-multiplying and solving for x, we get:

x = 125

So, the estimated turtle population for 2009 is 125.

For 2010:

Let y be the turtle population for 2010.
The proportion can be set up as:

tagged turtles in 2010 / total number of turtles in 2010 = tagged turtles in 2008 / total number of turtles in 2008

Plugging in the known values, we get:

8 / 30 = 40 / y

Cross-multiplying and solving for y, we get:

y = 150

So, the estimated turtle population for 2010 is 150.