Consider following parametric equations for a curve.

$x=e^{-4t}cos(4t),y=e^{-4t}sin(4t),z=e^{-4t}$

Determine the value of $t$ that corresponds to the point $(1,0,1).$

$t=$

$$

Write a vector equation $r(t)$ for the given curve.

$r(t)=$

Find $r^{\text{'}}(t).$

$r^{\text{'}}(t)=$

Find parametric equations for the tangent line to the curve with the