"The percentage of a model of a car that is still being driven after t years is estimated by mathematical model
y=100e ^ (-0.13853 t )
what percent of this type of car is still on the road after 12 years."
What you have is a function y of t where y is a percentage and t the time in years. So y depends on t.
I do not see any calculus in this problem. You have y(t)=100e ^ (-0.13853 t ) and you are looking for the percentage (i.e. y) after t=12 years so it is just plugging 12 in place of t in the function : y(t)=100e ^ (-0.13853 t ).
So : y(12)=100e ^ (-0.13853 *12) = 18.97 %.