2. 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
HELP MEE!!!!! I am stuck am 2010
To estimate the turtle population for 2009 using a proportion, you can set up a proportion based on the tagged turtles captured in 2009.
Let's say "x" is the estimated population for 2009. We know that 16 out of 50 turtles captured were tagged. So, we can set up the following proportion:
(turtles tagged in 2008)/(total population in 2008) = (turtles tagged in 2009)/(estimated population in 2009)
Plugging in the values, we get:
40/total population in 2008 = 16/x
To solve for "x", we can cross-multiply:
40x = 16 * (total population in 2008)
Divide both sides by 16:
x = (16 * total population in 2008)/40
Now, calculate the value of x using the given information for the total population in 2008.
To estimate the turtle population for 2010, we can follow a similar approach.
Let's say "y" is the estimated population for 2010. We know that 8 out of 30 turtles captured were tagged. So, we can set up the following proportion:
(turtles tagged in 2008)/(total population in 2008) = (turtles tagged in 2010)/(estimated population in 2010)
Plugging in the values, we get:
40/total population in 2008 = 8/y
To solve for "y", we can cross-multiply:
40y = 8 * (total population in 2008)
Divide both sides by 8:
y = (8 * total population in 2008)/40
Now, calculate the value of y using the given information for the total population in 2008.
We know that there are 40 turtles tagged.
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)