Let $y(t)be$ the solution $to{y}^{\text{'}}=\sqrt[\phantom{2}]{t+y}$ satisfying $y(3\mathrm{.}7)=2.$

Use Euler's Method with time step $h=0\mathrm{.}05to$ approximate $y(4).$

$(Use$ decimal notation. Give your answers $to$ four decimal places.$)$

$n=0,t_0=3\mathrm{.}7,y_0=$

$n=1,t_1=3\mathrm{.}75,y_1=$

$n=2,t_2=3\mathrm{.}8,y_2=$

$n=3,t_3=3\mathrm{.}85,y_3=$

$n=4,t_4=3\mathrm{.}9,y_4=$

$n=5,t_5=3\mathrm{.}95,y_5=$

$n=6,t_6=4,y_6=$