To determine how many marriage licenses were issued in Clark County, Nevada, in the year 2006, we use the given model:
[tex]\[ y = 3.4905x^2 - 17674x + 21533000 \][/tex]
where [tex]\( x \)[/tex] is the year, and [tex]\( y \)[/tex] is the number of marriage licenses issued.
First, substitute [tex]\( x = 2006 \)[/tex] into the model:
[tex]\[ y = 3.4905(2006)^2 - 17674(2006) + 21533000 \][/tex]
Perform the calculations step-by-step:
1. Calculate [tex]\( (2006)^2 \)[/tex]:
[tex]\[ 2006^2 = 4024036 \][/tex]
2. Multiply the result by 3.4905:
[tex]\[ 3.4905 \times 4024036 \approx 14037185.558 \][/tex]
3. Multiply [tex]\( 17674 \)[/tex] by [tex]\( 2006 \)[/tex]:
[tex]\[ 17674 \times 2006 \approx 35457724 \][/tex]
4. Subtract the second product from the first, along with adding the constant term:
[tex]\[ 14037185.558 - 35457724 + 21533000 \approx 124853.658 \][/tex]
So, according to the model, the number of marriage licenses issued in 2006 is approximately 124,853.658.
Next, we round this result to the nearest hundred:
- Looking at the decimal part (0.658), we round up since it is closer to 900 than 800.
Therefore, the rounded number of marriage licenses issued in 2006 is approximately 124,900.
Thus, the correct answer is:
C. 124,900
