in 2008 all 40 caught were tagged...
so... in 2009
16tags/50 caught = 40 tags/TOTAL
solving for x you obtain
(50x40) = 16(TOTAL)
2000 = 16(TOTAL) thus divide both sides by 16...
In 2009 there were 125 turtles
Now you try 2010...
a. use a proportion to estimate the turtle population for 2009
b. use a proportion to estimate the turtle population for 2010
so... in 2009
16tags/50 caught = 40 tags/TOTAL
solving for x you obtain
(50x40) = 16(TOTAL)
2000 = 16(TOTAL) thus divide both sides by 16...
In 2009 there were 125 turtles
Now you try 2010...
16T = 2000
T = 125
Yep! I got the same answer! :-)
In 2010, 8/30 = 26.7% of the population was tagged. So, the population is about 150 (P/40 = 30/8)
a. To estimate the turtle population for 2009:
We know that in 2008, the researcher tagged 40 giant turtles. In 2009, she captured 50 turtles, out of which 16 were tagged. We can set up a proportion to estimate the turtle population for 2009.
Let's represent the unknown population size for 2009 with "P":
(tagged turtles in 2009) / (total turtles captured in 2009) = (tagged turtles in 2008) / (total turtles tagged in 2008)
Using the information we have:
16 / 50 = 40 / P
Now let's solve for P:
16P = 50 * 40
16P = 2000
P = 2000 / 16
P = 125
The estimated turtle population for 2009 is 125.
b. To estimate the turtle population for 2010:
We know that in 2010, the researcher captured 30 turtles, out of which 8 were tagged. Again, we can set up a proportion to estimate the turtle population for 2010.
Let's represent the unknown population size for 2010 with "Q":
(tagged turtles in 2010) / (total turtles captured in 2010) = (tagged turtles in 2008) / (total turtles tagged in 2008)
Using the information we have:
8 / 30 = 40 / Q
Now let's solve for Q:
8Q = 30 * 40
8Q = 1200
Q = 1200 / 8
Q = 150
The estimated turtle population for 2010 is 150.