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.
a. use a proportion to estimate the turtle population for 2009
b. use a proportion to estimate the turtle population for 2010
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...
thank you i did it!!!!:)))))
Dear Ms Sue... please check my math... as it is late, and I may not truly be thinking straight :)
Excellent : )
16tags/50 caught = 40 tags/TOTAL
16T = 2000
T = 125
Yep! I got the same answer! :-)
And good night from southeastern Michigan! It was good to see something beautiful and positive today.
In 2009, 16/50 = 32% of the population was tagged, making the population 40/.32 = 125 (P/40 = 50/16)
In 2010, 8/30 = 26.7% of the population was tagged. So, the population is about 150 (P/40 = 30/8)
To estimate the turtle population for 2009 and 2010, we can use proportions based on the number of tagged turtles captured in each year.
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.