To estimate how many patrons borrow novels at the library, we first find the proportion of the surveyed patrons who borrow novels and then apply that proportion to the total number of patrons at the library.
The manager surveyed 80 patrons and found that 3 of them borrowed novels. The proportion of patrons borrowing novels in the survey can be calculated as follows:
\[ \text{Proportion of patrons borrowing novels} = \frac{\text{Number of patrons borrowing novels}}{\text{Total number of surveyed patrons}} = \frac{3}{80} \]
Now, we can use this proportion to estimate the number of patrons who borrow novels out of the total 345 patrons:
\[ \text{Estimated number of patrons borrowing novels} = \text{Total number of patrons} \times \text{Proportion of patrons borrowing novels} = 345 \times \frac{3}{80} \]
Calculating this gives:
\[ \text{Estimated number of patrons borrowing novels} = 345 \times 0.0375 = 12.9375 \]
Rounding this to the nearest whole number, we find:
\[ \text{Estimated number of patrons borrowing novels} \approx 13 \]
Thus, approximately 13 patrons borrow novels when they visit the library.