#### Answer

1. The explicit formula is A(n)=46.75-3.25(n-1)2. After 12 lunches, the card has $11.

#### Work Step by Step

1. The explicit formula is A(n)=46.75-3.25(n-1) because every time you buy lunch, the amount of money on the card decreases by 3.25 dollars and therefore the money in the card is decreasing by 3.25. Also the first term in the sequence is 46.75 because A(1) is 46.75 which is the amount money in the card after buying one lunch as the card had 50 dollars before any transaction.
2. After 12 lunches, the card has $11. To solve this we will plug in n=12 in
A(12)=46.75-3.25(12-1)=46.75-3.25(11)= 46.75-35.75= 11