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.
Use a proportion to estimate the turtle population for 2009.
Use a proportion to estimate the turtle population for 2010..
For 2009:
Let x be the turtle population for 2009.
The proportion can be set up as:
tagged turtles in 2009 / total number of turtles in 2009 = tagged turtles in 2008 / total number of turtles in 2008
Plugging in the known values, we get:
16 / 50 = 40 / x
Cross-multiplying and solving for x, we get:
x = 125
So, the estimated turtle population for 2009 is 125.
For 2010:
Let y be the turtle population for 2010.
The proportion can be set up as:
tagged turtles in 2010 / total number of turtles in 2010 = tagged turtles in 2008 / total number of turtles in 2008
Plugging in the known values, we get:
8 / 30 = 40 / y
Cross-multiplying and solving for y, we get:
y = 150
So, the estimated turtle population for 2010 is 150.
To estimate the turtle population for 2009 using a proportion, we can set up the following proportion:
(Number of tagged turtles in 2009) / (Total number of turtles captured in 2009) = (Number of tagged turtles in 2008) / (Total population of turtles in 2008)
Let's substitute the given values into this proportion:
(16) / (50) = (40) / (x)
To solve for x, we can cross-multiply:
16 * x = 40 * 50
16x = 2000
Divide both sides by 16 to isolate x:
x = 2000 / 16
x = 125
So, we can estimate that the turtle population in 2009 was approximately 125.
Now, let's estimate the turtle population for 2010 using a similar proportion:
(Number of tagged turtles in 2010) / (Total number of turtles captured in 2010) = (Number of tagged turtles in 2008) / (Total population of turtles in 2008)
Substituting the given values:
(8) / (30) = (40) / (x)
Cross-multiplying:
8 * x = 40 * 30
8x = 1200
Dividing by 8:
x = 1200 / 8
x = 150
Therefore, we can estimate that the turtle population in 2010 was approximately 150.