For a smooth curve $C$ represented by the parametric equations $x=x(t),y=y(t),atb,$ the arc length $s$ satisfies the equation

$\frac{ds}{dt}=\sqrt[\phantom{2}]{(\frac{dx}{dt}{)}^2+(\frac{dy}{dt}{)}^2}$

In terms of differentials, this can be written as

$ds=\sqrt[\phantom{2}]{(dx{)}^2+(dy{)}^2}$

The differential $ds$ can be used to approximate the arc length $s$ between two nearby points.

Use the differential $ds$ to approximate the arc length of the curve

$x(t)=e^{4t},y(t)=e^{2t}$

from $t=0$ to $t=0\mathrm{.}2.$

$($Use decimal notation. Give your answer to two decimal places.$)$

$s$~~