- Calculate the food percentage for each flock: \(\text{Percentage} = (\frac{\text{Pieces}}{300}) \times 100\).
- Determine the simulated number of birds for each: \(\text{Birds} = \text{Percentage (as decimal)} \times 30\).
- Verify that percentages sum to 100% and bird counts sum to 30.
- Final values: Food Percentages \(\boxed{19\%, 51\%, 30\%}\); Simulated Birds \(\boxed{5.7, 15.3, 9}\).
Explanation
- Data and Problem Analysis
The problem asks us to determine the food percentage and the simulated number of birds for three distinct flocks of birds (X, Y, and Z) based on the amount of food they consumed. We are given that the total pieces of food consumed by all three flocks combined is 300, and the total population for the next generation is 30 birds. The food consumption for each flock is provided:
- Flock X: 57 pieces
- Flock Y: 153 pieces
- Flock Z: 90 pieces
To find the food percentage, we divide each flock's individual consumption by the total consumption (300) and multiply by 100. Then, to find the simulated number of birds for each flock, we multiply the calculated percentage (as a decimal) by the total number of birds (30).
- Calculations and Results
We first calculate the food percentage for each flock:
- For Flock X: \(\frac{57}{300} \times 100 = 19\%\).
- For Flock Y: \(\frac{153}{300} \times 100 = 51\%\).
- For Flock Z: \(\frac{90}{300} \times 100 = 30\%\).
Next, we calculate the simulated number of birds in the 2nd generation for each flock:
- For Flock X: \(0.19 \times 30 = 5.7\).
- For Flock Y: \(0.51 \times 30 = 15.3\).
- For Flock Z: \(0.30 \times 30 = 9\).
As a check, we sum the percentages (\(19\% + 51\% + 30\% = 100\%\)) and the number of birds (\(5.7 + 15.3 + 9 = 30\)). Both sums are correct.
- Summary and Conclusion
Based on our calculations, the completed table is as follows:
| Flock X | Flock Y | Flock Z \) Total Pieces of Food Eaten | \(57\) | \(153\) | \(90\) \) Food Percentage | \(19\%\) | \(51\%\) | \(30\%\) \) Simulated Number of Birds | \(5.7\) | \(15.3\) | \(9\) \) |
The final values for the food percentages are \(\boxed{19\%, 51\%, 30\%}\) and the simulated number of birds are \(\boxed{5.7, 15.3, 9}\).
Examples
Understanding resource distribution is crucial in biology and ecology, particularly when studying how animals allocate food to population growth. For instance, wildlife biologists often use the proportion of resources consumed by specific groups within a population to predict the next generation's distribution. This simple mathematical model allows researchers to estimate population shifts based on energy intake, helping them manage conservation efforts and habitat sustainability effectively.