To find your explicit rule, you would make your function (f(n)) equal to your change in cards per month (24) times your number of months (n) plus you initial number of cards (523). This creates the function f(n)=24n+523. What this is essentially doing is calculating the number of new cards bought in n months (24n) and adding it to your starting value (523) to get your new number of cards (f(n)).
