It truly helps if you follow standard notation if only for communication with others. I find it also prevents me from making silly mistakes.
You are left with a simple exponential equation. You may need to review them from back in algebra.
[MATH]S = 0.5S_0 \implies 0.5S_0 = S_0e^{-at} \implies e^{-at} = 0.5 \implies\\ ln(e^{-at}) = ln(0.5) \implies (-at)ln(e) = ln(0.5) \implies\\ -at * 1 = ln(0.5) \implies t = - \dfrac{ln(0.5)}{a}.[/MATH]Does the sign of that answer make sense?
You are left with a simple exponential equation. You may need to review them from back in algebra.
[MATH]S = 0.5S_0 \implies 0.5S_0 = S_0e^{-at} \implies e^{-at} = 0.5 \implies\\ ln(e^{-at}) = ln(0.5) \implies (-at)ln(e) = ln(0.5) \implies\\ -at * 1 = ln(0.5) \implies t = - \dfrac{ln(0.5)}{a}.[/MATH]Does the sign of that answer make sense?