Setting:
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.

questions to
a.) use a proportion to estimate the turtle population for 2009.
b.) use a proportion to estimate the turtle population for 2010.

How much did the ratio change for 2009 and 2010, say there's a linear change between the years so how much did it change from 2008 to 2009...

organize your information... tagged *2008: 40 *2009: 16 *2010: 8 total caught *2009: 50 *2010: 30 Now, you can compare them. Like so, let's use the first one. You can compare the ratio of 16/40 = 50 / x where x is the total population so basically, the proportion above represents that 16 of the 40 tagged were caught and it relates proportionately to the number of turtles caught out of the entire population of turtles that were currently there in 2009. Now, you can cross multiply to get this... 16/40= 50/x 16x = 2000 then divide by 16 x = 125 125 represents the total population Set up the other proportion just likes this and you should be able to get the population for 2010 as well. There are other ways to set it up though if you want to experiment on your own. Hope this helped.