Question 1036508
I think you meant {{{ r(t) = e^t* i + (2/9) e^(2t)* j }}}, which is a vector-valued function.
Let {{{x = e^t}}} and {{{y = (2/9) e^(2t)}}} as they were meant to be.

Then after a simple substitution, you should get {{{y=(2/9) (e^t)^2 = (2/9)x^2}}}.

{{{ Velocity = e^t*i + (4/9)e^(2t)*j }}}

{{{ Acceleration = e^t*i + (8/9)e^(2t)*j }}}