Let's analyze the given table and the equations provided in the question. We need to verify which equation fits the table for [tex]\( n = 5 \)[/tex].
The table shows:
- For [tex]\( n = 5 \)[/tex]
We need to verify it against the given [tex]\( n \)[/tex]. Examining the options:
First, compute [tex]\( n^2 \)[/tex] for [tex]\( n = 5 \)[/tex]:
[tex]\[ n^2 = 5^2 = 25 \][/tex]
Next, we evaluate each proposed equation with [tex]\( n = 5 \)[/tex]:
1. [tex]\( n^2 + 3n + 40 \)[/tex]
[tex]\[ 25 + 3(5) + 40 = 25 + 15 + 40 = 80 \][/tex]
2. [tex]\( n^2 + 13n + 40 \)[/tex]
[tex]\[ 25 + 13(5) + 40 = 25 + 65 + 40 = 130 \][/tex]
3. [tex]\( n^2 + 40n + 13 \)[/tex]
[tex]\[ 25 + 40(5) + 13 = 25 + 200 + 13 = 238 \][/tex]
4. [tex]\( n^2 + 40n + 3 \)[/tex]
[tex]\[ 25 + 40(5) + 3 = 25 + 200 + 3 = 228 \][/tex]
Given these results:
- Option 1 results in 80
- Option 2 results in 130
- Option 3 results in 238
- Option 4 results in 228
We observe that option matching our calculations:
1. [tex]\( n^2 + 3n + 40 = 80 \)[/tex]
2. [tex]\( n^2 + 13n + 40 = 130 \)[/tex]
3. [tex]\( n^2 + 40n + 13 = 238 \)[/tex]
4. [tex]\( n^2 + 40n + 3 = 228 \)[/tex]
Since the table entry for [tex]\( n = 5 \)[/tex] and 40 should match one of these results, the correct equation represented by Ms. Wilson's model is the one that meets the calculations.
Hence the correct equation is:
[tex]\[ n^2 + 3n + 40 = 80 \][/tex]
