Step 1 :Given the polynomial $2+1.43 x+0.21 y$, where $x$ is the number of miles driven and $y$ is the time in minutes for the ride.
Step 2 :We are asked to evaluate the polynomial for $x=13$ and $y=26$.
Step 3 :Substitute the given values of $x$ and $y$ into the polynomial to find the cost of the cab ride.
Step 4 :The cost of the cab ride is calculated as $2+1.43(13)+0.21(26)$.
Step 5 :After calculating, we find that the cost of the cab ride is $26.05$.
Step 6 :Interpret the answer in the context of this problem: This means it costs \(\boxed{26.05}\) dollars for a 13 mile cab ride that lasts 26 minutes.