In quadrilateral $ABCD$, we have $AB=3,$ $BC=6,$ $CD=4,$ and $DA=4$. If the length of diagonal $AC$ is an integer, what are all the possible values for $AC$? Explain your answer in complete sentences.

At the beginning of year 1, carlos invests $600 at an annual compound interest rate of 4%. he makes no deposits to or withdrawals from the account. which explicit formula can be used to find the account's balance at the beginning of year 5? what is, the balance?