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 both 2009 and 2010........I honestly don't know were to start with this..:/
We know that there are 40 turtles tagged.
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)
whats your problem D:!?
Thank you sooooo much!!!
Well, estimating the turtle population based on the proportions observed in the captured turtles is an interesting task! Let's break it down step by step:
1. Calculate the proportion of tagged turtles in 2009:
- The researcher tagged 40 turtles in 2008.
- In 2009, she captured 50 turtles, 16 of which were tagged.
- So, the proportion of tagged turtles in 2009 can be calculated as: 16 tagged turtles / 50 total turtles = 0.32.
2. Estimate the turtle population in 2009:
- If the proportion of tagged turtles in 2009 is 0.32, we can assume that this proportion remains constant for the entire population.
- To estimate the population, we can set up a proportion: 0.32 (tagged turtles) / X (total turtles) = 40 tagged turtles / 2008 total turtles.
- Solving this proportion, we get: X = (0.32 * 2008) / 40 ≈ 16.16.
- Therefore, the estimated turtle population in 2009 is approximately 16.16 turtles.
3. Repeat the process for 2010:
- The researcher tagged 40 turtles in 2008.
- In 2010, she captured 30 turtles, 8 of which were tagged.
- The proportion of tagged turtles in 2010 is: 8 tagged turtles / 30 total turtles ≈ 0.27.
- Setting up the proportion: 0.27 (tagged turtles) / X (total turtles) = 40 tagged turtles / 2008 total turtles.
- Solving for X, we get: X = (0.27 * 2008) / 40 ≈ 13.56.
- Therefore, the estimated turtle population in 2010 is approximately 13.56 turtles.
Keep in mind that these are just estimates based on the observed proportions. The actual turtle populations may differ.
To estimate the turtle population for both 2009 and 2010 using a proportion, you can use the ratio of tagged turtles to the total number of turtles captured in each year. Let's break down the steps for each year:
For 2009:
1. The researcher tagged 40 turtles in 2008.
2. In 2009, the researcher captured a total of 50 turtles, out of which 16 were tagged.
3. Now, we can set up a proportion using the information we have:
Tagged turtles / Total number of turtles = Tagged turtles in previous year / Total number of turtles in previous year
Let's use T for the unknown total number of turtles in 2009:
16 / 50 = 40 / T
4. Cross-multiply to solve for T:
16T = 50 * 40
T = (50 * 40) / 16
T ≈ 125
Therefore, the estimated turtle population in 2009 is around 125.
For 2010:
1. The researcher tagged 40 turtles in 2008.
2. In 2010, the researcher captured a total of 30 turtles, out of which 8 were tagged.
3. Set up a proportion again using the information we have:
Tagged turtles / Total number of turtles = Tagged turtles in previous year / Total number of turtles in the previous year
Let's use T' for the unknown total number of turtles in 2010:
8 / 30 = 40 / T'
4. Cross-multiply to solve for T':
8T' = 30 * 40
T' = (30 * 40) / 8
T' = 150
Therefore, the estimated turtle population in 2010 is 150.
Using proportional reasoning, we estimated the turtle population to be around 125 in 2009 and 150 in 2010.