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
Can someone explain this as simply as possible? Im failing in math and i really want to understand the answer :)
When a math tutor comes online, he/she will help.
Patience!
I am being patient..?
look at Steve' solution to the same question:
http://www.jiskha.com/display.cgi?id=1367836044
To estimate the turtle population for 2009 and 2010, we can use the method of proportion. The idea is to assume that the proportion of tagged turtles to the total captured turtles in a given year is equal to the proportion of tagged turtles to the total population of turtles in that year.
a: To estimate the turtle population for 2009, we know that in that year the researcher captured a total of 50 turtles, out of which 16 were tagged. We can set up a proportion as follows:
Number of tagged turtles in 2009 / Total number of turtles captured in 2009 = Number of tagged turtles in the entire population / Total turtle population in 2009
16 / 50 = x / P (where P represents the total turtle population in 2009)
To solve for P, we can cross-multiply and solve for x:
16 * P = 50 * x
P = (50 * x) / 16
Using this proportion, we can estimate the turtle population for 2009.
b: Similarly, to estimate the turtle population for 2010, we know that in that year the researcher captured a total of 30 turtles, out of which 8 were tagged. We can set up the following proportion:
Number of tagged turtles in 2010 / Total number of turtles captured in 2010 = Number of tagged turtles in the entire population / Total turtle population in 2010
8 / 30 = x / P (where P represents the total turtle population in 2010)
By cross-multiplying and solving for x, we can estimate the turtle population for 2010.
It's important to note that these estimates are based on the assumption that the proportion of tagged turtles in the researcher's sample is representative of the whole population. The actual population size may vary, but this method provides a reasonable estimate.