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.
thank you but I don't get it
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)
16/50 = 40/x
16x = 2000
x = 125
Do the same for 2010.
To estimate the turtle population for 2009 and 2010 using proportions, we can set up ratios comparing the number of tagged turtles to the total population.
A. Estimating the turtle population for 2009:
In 2008, the researcher tagged 40 turtles, and in 2009, out of the 50 turtles captured, 16 were tagged.
To estimate the population of turtles for 2009 using a proportion, we can set up the following ratio:
Tagged turtles in 2009 / Total turtle population in 2009 = Tagged turtles in 2008 / Total turtle population in 2008
Let 'x' represent the total turtle population in 2009:
16 / 50 = 40 / x
Cross-multiplying:
16x = 50 * 40
16x = 2000
Dividing both sides of the equation by 16:
x = 2000 / 16
x = 125
The estimated turtle population for 2009 is 125.
B. Estimating the turtle population for 2010:
In 2008, the researcher tagged 40 turtles, and in 2010, out of the 30 turtles captured, 8 were tagged.
To estimate the population of turtles for 2010 using a proportion, we can set up the following ratio:
Tagged turtles in 2010 / Total turtle population in 2010 = Tagged turtles in 2008 / Total turtle population in 2008
Let 'y' represent the total turtle population in 2010:
8 / 30 = 40 / y
Cross-multiplying:
8y = 30 * 40
8y = 1200
Dividing both sides of the equation by 8:
y = 1200 / 8
y = 150
The estimated turtle population for 2010 is 150.