Step 1 :The question is asking for the stopping distance of a car traveling at 40 mph. The formula for stopping distance is given as \(d(v)=1.3 v+0.04 v^2\). We can substitute \(v=40\) into this formula to find the stopping distance.
Step 2 :Substitute \(v=40\) into the formula: \(d = 1.3(40) + 0.04(40^2)\)
Step 3 :Solve the equation to find the stopping distance: \(d = 116.0\)
Step 4 :Round the stopping distance to the nearest foot: \(d = 116\)
Step 5 :Final Answer: It will take \(\boxed{116}\) feet to stop the car that is traveling at \(40 \mathrm{mph}\).