Voter Prediction 709E12

1. **State the problem:** We want to predict the number of voters in the 7th town council election based on the given data of total residents and voters for elections 1 through 6. 2. **Analyze the data:** We have the following pairs of total residents ($R$) and voters ($V$): $$ \begin{aligned} & (3511, 386), (3790, 414), (4085, 451), (4907, 544), (5562, 623), (7014, 767) \end{aligned} $$ 3. **Find the ratio of voters to residents for each election:** $$ \frac{386}{3511} \approx 0.110\quad \frac{414}{3790} \approx 0.109\quad \frac{451}{4085} \approx 0.110\quad \frac{544}{4907} \approx 0.111\quad \frac{623}{5562} \approx 0.112\quad \frac{767}{7014} \approx 0.109 $$ 4. **Calculate the average voter turnout ratio:** $$ \text{Average ratio} = \frac{0.110 + 0.109 + 0.110 + 0.111 + 0.112 + 0.109}{6} = \frac{0.661}{6} \approx 0.1102 $$ 5. **Use the average ratio to predict voters in the 7th election:** Given total residents in 7th election $R_7 = 7786$, predicted voters $V_7$ is: $$ V_7 = 0.1102 \times 7786 \approx 857.9 $$ 6. **Round to the nearest whole number:** $$ V_7 \approx 858 $$ **Final answer:** We expect approximately **858** voters in the 7th town council election.