Step 1 :The question is asking for the average score when the students initially took the test. This corresponds to the time \(t=0\). We can substitute \(t=0\) into the equation \(S(t)=77-14 \ln (t+1)\) to find the initial average score.
Step 2 :Substitute \(t=0\) into the equation: \(S(0)=77-14 \ln (0+1)\)
Step 3 :Calculate the value of \(S(0)\) to get the initial average score.
Step 4 :The average score when they initially took the test was \(\boxed{77.0\%}\).