jmc

If $n$ days have passed since Sunday, then the total number of cents in her bank account is $1+2+\cdots +2^n$. This is a geometric series with first term 1, common ratio 2 and $n+1$ terms. Hence the sum is: $$1+2+\cdots +2^n=\frac{1-2^{n+1}}{1-2}=2^{n+1}-1.$$If this is greater than $500$ (i.e. if the total amount of money in the account is more than \5$)then$2^{n+1}-1\ge 500$,so$2^{n+1}\ge 501$.Thesmallestpowerof2thatisgreaterthan501is$2^9$.Thusthefirsttimethereismorethan$\$5$ in the bank account occurs after $n=8$ days. This is 8 days away from Sunday, so the day of the week is $\boxed{\text{Monday}}$.