Maximize expected wealth or growth?

A coin lands heads with probability $0.6$. You may bet any fraction $f$ of your current wealth on heads at even money, and you will make 100 bets using the same $f$ each time. (a) Which $f$ maximizes expected final wealth, and what is the catch? (b) Which $f$ maximizes the long-run growth rate? (c) Compare final wealth under $f = 0.2$ and $f = 0.4$ on a path with 60 wins and 40 losses.