For the function $N(t) = 75 + 10t$, which models an account starting with $75$ unread emails and growing by $10$ emails per day, the number of unread emails is a function of the number of days. The number of unread emails, $N$, depends on the number of days, $t$. Therefore, the variable $N$ acts as the dependent variable, while the variable $t$ serves as the independent variable.