- Calculate the food percentage for each flock by dividing its food consumption by the total food of 300 pieces and multiplying by 100: \(P_X = \frac{32}{300} \times 100 = 10.67\%\), \(P_Y = \frac{180}{300} \times 100 = 60\%\), \(P_Z = \frac{88}{300} \times 100 = 29.33\%\).
- Calculate the simulated number of birds by multiplying the food percentage by the total bird count of 30: \(N_X = 3.2\), \(N_Y = 18\), \(N_Z = 8.8\).
- The completed table values for (Food %, Simulated Birds) are: Flock X \((\boxed{10.67\%}, \boxed{3.2})\), Flock Y \((\boxed{60\%}, \boxed{18})\), and Flock Z \((\boxed{29.33\%}, \boxed{8.8})\).
Explanation
- Problem Analysis and Data Overview
We are provided with food consumption data for three bird flocks (X, Y, and Z). The total food consumed across all three flocks is given as 300 pieces. We need to determine the food percentage for each flock, calculated as the flock's food consumption divided by the total consumption, and then determine the simulated number of birds for each flock by multiplying that percentage by the total number of 30 birds.
The data is as follows:
- Flock X: 32 pieces of food
- Flock Y: 180 pieces of food
- Flock Z: 88 pieces of food
Total food = 300 pieces.
Total birds = 30.
- Calculating Food Percentages
To find the food percentage for each flock, we use the formula \(\text{Food Percentage} = \frac{\text{Pieces of Food}}{\text{Total Pieces of Food}} \times 100\%\).
- For Flock X: \(\frac{32}{300} \times 100\% = \frac{32}{3}\% \approx 10.67\%\).
- For Flock Y: \(\frac{180}{300} \times 100\% = \frac{180}{3}\% = 60\%\).
- For Flock Z: \(\frac{88}{300} \times 100\% = \frac{88}{3}\% \approx 29.33\%\).
Note that these percentages sum to \(\frac{32+180+88}{3}\% = \frac{300}{3}\% = 100\%\), confirming our calculations are accurate.
- Calculating Simulated Number of Birds
To find the simulated number of birds, we multiply the food percentage of each flock by the total population of 30 birds. The formula is \(\text{Simulated Number} = \frac{\text{Food Percentage}}{100} \times 30\). This is equivalent to \(\frac{\text{Pieces of Food}}{\text{Total Pieces}} \times 30 = \frac{\text{Pieces of Food}}{10}\).
- For Flock X: \(\frac{32}{10} = 3.2\).
- For Flock Y: \(\frac{180}{10} = 18\).
- For Flock Z: \(\frac{88}{10} = 8.8\).
The sum of these simulated numbers is \(3.2 + 18 + 8.8 = 30\), which matches the total population of birds.
- Final Results Summary
We can now populate the table with our results.
The food percentages are:
- Flock X: \(10.67\%\) (or \(32/3\%\))
- Flock Y: \(60\%\)
- Flock Z: \(29.33\%\) (or \(88/3\%\))
The simulated number of birds are:
- Flock X: \(3.2\)
- Flock Y: \(18\)
- Flock Z: \(8.8\)
Final values for the table:
Flock X: \(10.67\%\) and \(3.2\)
Flock Y: \(60\%\) and \(18\)
Flock Z: \(29.33\%\) and \(8.8\)
Examples
In biological field studies, researchers often use food consumption or energy intake as a proxy to estimate the distribution of animals within a population when direct counts are difficult. By measuring the resources consumed by different subgroups (like flocks or families), scientists can proportionalize the total population to understand group dynamics and resource requirements. This helps in conservation efforts where accurate monitoring of how different sub-populations interact with their environment is essential.