Using S$.$I Units, determine respective units for $a,b,c$ and $y$ in the dimensionally homogeneaous equation:

$y=A{e}^{-bt}cos[\sqrt[\phantom{2}]{1-a^2}bt+c]$ in which $A$ is a length and $t$ is time

$\backslash$table$[[A,t,a,b,c$