Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
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.
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To estimate the turtle population for 2009 and 2010 using a proportion, we can use the information provided.
Let's start with estimating the turtle population for 2009:
Step 1: Determine the proportion of tagged turtles in 2009.
In 2009, the researcher captured 50 turtles, 16 of which were tagged. So, the proportion of tagged turtles is:
Proportion of tagged turtles in 2009 = (Number of tagged turtles in 2009) / (Total number of turtles captured in 2009)
Proportion of tagged turtles in 2009 = 16 / 50
Step 2: Apply the proportion to estimate the total turtle population in 2009.
To estimate the total turtle population in 2009, we set up a proportion using the proportion from step 1:
Proportion of tagged turtles in 2009 = (Number of tagged turtles in 2008) / (Total turtle population in 2008)
16 / 50 = 40 / X (where X is the total turtle population in 2008)
Step 3: Solve the proportion to estimate the turtle population in 2009.
We can cross multiply and solve for X:
16 * X = 40 * 50
X = (40 * 50) / 16
By evaluating the above calculation, we can estimate the turtle population in 2009.
Similarly, we can estimate the turtle population for 2010:
Step 1: Determine the proportion of tagged turtles in 2010.
In 2010, the researcher captured 30 turtles, 8 of which were tagged. So, the proportion of tagged turtles is:
Proportion of tagged turtles in 2010 = (Number of tagged turtles in 2010) / (Total number of turtles captured in 2010)
Proportion of tagged turtles in 2010 = 8 / 30
Step 2: Apply the proportion to estimate the total turtle population in 2010.
To estimate the total turtle population in 2010, we set up a proportion using the proportion from step 1:
Proportion of tagged turtles in 2010 = (Number of tagged turtles in 2009) / (Total turtle population in 2009)
8 / 30 = 16 / X (where X is the total turtle population in 2009)
Step 3: Solve the proportion to estimate the turtle population in 2010.
We can cross multiply and solve for X:
8 * X = 16 * 30
X = (16 * 30) / 8
By evaluating the above calculation, we can estimate the turtle population in 2010.
Please note that these estimates are based on the assumption of proportional behavior of the turtle population, and may not represent the actual population.