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Step 5: Use the Data to Model the Sizes of the Flocks in the Second Generation

\begin{tabular}{|l|l|l|l|}
\cline{2-4}
\multicolumn{1}{c|}{} & Flock X & Flock Y & Flock Z \\
\hline
\begin{tabular}{l}
Total Pieces of Food Eaten \\
(from previous page)
\end{tabular} & 123 & 99 & 78 \\
\hline
Food Percentage & & & \\
\hline
Simulated Number of Birds in Flock for 2nd Generation & & & \\
\hline
\end{tabular}

Divide each flock's total pieces of food by 300, the total number of pieces of food eaten.
 Multiply the food percentage for each flock by the total number of birds (30).



Answer :

GinnyAnswer
Alright, let's detail out the steps and fill in the missing parts in your table based on the provided data.

### Given Data:
- Total pieces of food eaten by all flocks = 300
- Total initial number of birds = 30
- Pieces of food eaten by Flock X = 123
- Pieces of food eaten by Flock Y = 99
- Pieces of food eaten by Flock Z = 78

We need to calculate the food percentage for each flock and then use these percentages to model the sizes of the flocks in the second generation.

#### Step-by-Step Calculations:

#### 1. Calculate the Food Percentage for Each Flock

- Flock X:
[tex]\[ \text{Food Percentage (Flock X)} = \frac{\text{Pieces of Food Eaten by Flock X}}{\text{Total Pieces of Food Eaten}} = \frac{123}{300} = 0.41 \][/tex]

- Flock Y:
[tex]\[ \text{Food Percentage (Flock Y)} = \frac{\text{Pieces of Food Eaten by Flock Y}}{\text{Total Pieces of Food Eaten}} = \frac{99}{300} = 0.33 \][/tex]

- Flock Z:
[tex]\[ \text{Food Percentage (Flock Z)} = \frac{\text{Pieces of Food Eaten by Flock Z}}{\text{Total Pieces of Food Eaten}} = \frac{78}{300} \approx 0.26 \][/tex]

#### 2. Calculate the Simulated Number of Birds in Each Flock for the Second Generation

- Flock X:
[tex]\[ \text{Simulated Number of Birds (Flock X) for 2nd Generation} = \text{Food Percentage (Flock X)} \times \text{Total Number of Birds} = 0.41 \times 30 = 12.3 \][/tex]

- Flock Y:
[tex]\[ \text{Simulated Number of Birds (Flock Y) for 2nd Generation} = \text{Food Percentage (Flock Y)} \times \text{Total Number of Birds} = 0.33 \times 30 = 9.9 \][/tex]

- Flock Z:
[tex]\[ \text{Simulated Number of Birds (Flock Z) for 2nd Generation} = \text{Food Percentage (Flock Z)} \times \text{Total Number of Birds} = 0.26 \times 30 \approx 7.8 \][/tex]

### Completed Table

Here is the completed table with the calculated values:

[tex]\[ \begin{tabular}{|l|l|l|l|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & \textbf{Flock X} & \textbf{Flock Y} & \textbf{Flock Z} \\ \hline \text{Total Pieces of Food Eaten} & 123 & 99 & 78 \\ \hline \text{Food Percentage} & 0.41 & 0.33 & 0.26 \\ \hline \begin{tabular}{l} \text{Simulated Number of} \\ \text{Birds in Flock for 2nd Generation} \end{tabular} & 12.3 & 9.9 & 7.8 \\ \hline \end{tabular} \][/tex]
These values accurately reflect the sizes of the flocks in the second generation based on their food consumption and the initial population.