Let $f$ be a real-valued continuous function on the interval $[0,1]$ and satisfy the following estimate $$ \left|\int_0^1 f(t) e^{st}dt\right|\le Cs^{\frac12},\quad s>1, $$ where the constant $C$ is independent of $s$. Can we assert that $f$ is identically zero on $[0,1]$?