Let's solve the question step by step:
1. Determine the population of Sherwood:
The population of Sherwood is given as 32,404.
2. Calculate half the population of Sherwood:
To find half the population of Sherwood, we divide 32,404 by 2:
[tex]\[
\frac{32,404}{2} = 16,202
\][/tex]
3. Formulate the condition for Baker's population:
The population of Baker (denoted as [tex]\( P \)[/tex]) is at least half the population of Sherwood. In mathematical terms, "at least" translates to a greater than or equal to ( [tex]\(\geq\)[/tex] ) expression.
Therefore, we have:
[tex]\[
P \geq 16,202
\][/tex]
4. Evaluate the given options based on this condition:
- [tex]\(P \geq 16,202\)[/tex]: This option states that the population of Baker is greater than or equal to 16,202, which is correct according to our calculation.
- [tex]\(P > 16,202\)[/tex]: This option states that the population of Baker is strictly greater than 16,202. It does not include the possibility of [tex]\( P \)[/tex] being exactly 16,202, so this is incorrect based on the condition given.
- [tex]\(P \geq 64,808\)[/tex]: This option states that the population of Baker is greater than or equal to 64,808, which is not correct since half the population of Sherwood is only 16,202.
- [tex]\(P < 16,202\)[/tex]: This option states that the population of Baker is less than 16,202, which contradicts the condition that the population should be at least half the population of Sherwood. Thus, it is incorrect.
From the evaluation, the correct inequality representing the population of Baker is:
[tex]\[
P \geq 16,202
\][/tex]
