Continuously compounded returns for an asset that increases in price from S1 to S2 over...

Choice 'd' is the correct answer. Continuously compounded returns are given by the log of S2/S1. The expression (S2 - S1)/S1 gives discrete returns, not continuously compounded returns.

Note that the question is only asking for the return over the given time period, not annualized returns. So t is not relevant here. If we had to find annualized returns, and t were expressed in years, then the annualized return would have been (1/t)*ln(S2/S1).

Also refer to the tutorial on interest rates and compounding for more information on continuously compounded rates.