An xy "Parametric Equations Known" Problem (Solution)

Problem 1: An x slider's position is known to be x = 4t² m, and a y slider's position is y = 2e^t m.  A pen is located at the intersection of the two sliders.  Do the following:
(a)  Eliminate t to obtain the x-y path equation of the pen.
At t = 3 sec, determine:
(b)  The pen's velocity, v, as a vector.
(c)  The pen's acceleration, a, as a vector.
(d)  The normal ( a_n ) and tangential ( a_t ) components of acceleration of the pen.