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.
1. Use a proportion to estimate the turtle population for 2009.
2. Use a proportion to estimate the turtle population for 2010.
1. The proportion can be set up as follows:
tagged turtles in 2009 / total turtles captured in 2009 = tagged turtles in 2008 / total population in 2008
Simplifying this proportion, we get:
16/50 = 40/x
where x is the estimated total population in 2009. We can cross-multiply and solve for x:
16x = 2000
x = 125
Therefore, we can estimate that there were 125 giant turtles in the population in 2009.
2. The proportion for 2010 can be set up similarly:
tagged turtles in 2010 / total turtles captured in 2010 = tagged turtles in 2008 / total population in 2008
Simplifying the proportion:
8/30 = 40/x
Cross-multiplying and solving for x:
8x = 1200
x = 150
Thus, we can estimate that there were 150 giant turtles in the population in 2010.
To estimate the turtle population for 2009 and 2010 using proportions, we can set up the following proportions:
1. For 2009:
Let x be the estimated turtle population in 2009.
The proportion would be: (Number of tagged turtles in 2009) / (Total captured turtles in 2009) = (Number of tagged turtles in 2008) / (Total turtle population in 2008)
Plugging in the given values: 16/50 = 40/x
2. For 2010:
Let y be the estimated turtle population in 2010
The proportion would be: (Number of tagged turtles in 2010) / (Total captured turtles in 2010) = (Number of tagged turtles in 2008) / (Total turtle population in 2008)
Substituting the given values: 8/30 = 40/y
Now, we can solve these proportions to estimate the turtle population for each year.
1. For 2009:
16/50 = 40/x
Cross multiply: 16x = 40 * 50
Simplify: 16x = 2000
Divide both sides by 16: x ≈ 125
The estimated turtle population in 2009 is approximately 125 turtles.
2. For 2010:
8/30 = 40/y
Cross multiply: 8y = 40 * 30
Simplify: 8y = 1200
Divide both sides by 8: y = 150
The estimated turtle population in 2010 is 150 turtles.
To estimate the turtle population for 2009 and 2010, you can use a proportion by comparing the ratio of tagged turtles to the total number of captured turtles in each year.
Let's start with estimating the turtle population for 2009:
Step 1: Set up a proportion using the number of tagged turtles from 2009 and the total number of captured turtles from 2009.
Tagged turtles in 2009 / Total captured turtles in 2009 = Tagged turtles in 2008 / Unknown total turtle population in 2008
16 / 50 = 40 / x
Step 2: Cross multiply and solve for x.
16x = 40 * 50
16x = 2000
x = 2000 / 16
x ≈ 125
Based on this proportion, we estimate that the turtle population in 2008 was approximately 125.
Now let's move on to estimating the turtle population for 2010:
Step 1: Set up a proportion using the number of tagged turtles from 2010 and the total number of captured turtles from 2010.
Tagged turtles in 2010 / Total captured turtles in 2010 = Tagged turtles in 2008 / Unknown total turtle population in 2008
8 / 30 = 40 / x
Step 2: Cross multiply and solve for x.
8x = 40 * 30
8x = 1200
x = 1200 / 8
x = 150
Based on this proportion, we estimate that the turtle population in 2010 was approximately 150.