A researcher tagged 40 giant turtles in 2008. In 2009, she returned and capture 50 turtles, 16 of which were tagged. And 2010, she returned again and captured 30 turtles, eight of which were tagged.
a) use a proportion to estimate the total population for 2009
b) use a proportion to estimate the total population for 2010
a) We can set up a proportion with the known tagged turtles in 2009 and the unknown total population for 2009:
16/50 = 40/x
We can cross-multiply and solve for x, which represents the estimated total population for 2009:
16x = 50*40
x = 125
Therefore, the estimated total population for 2009 is 125 giant turtles.
b) We can set up a similar proportion with the known tagged turtles in 2010 and the unknown total population for 2010:
8/30 = 40/x
Again, we can cross-multiply and solve for x:
8x = 30*40
x = 150
Therefore, the estimated total population for 2010 is 150 giant turtles.