Step 1 :The question is asking for the percentage of the target audience that buys the game without seeing a TV ad. This corresponds to the value of P when x=0. We can substitute x=0 into the equation to find this value.
Step 2 :Substitute x=0 into the equation: \(P(x)=\frac{100}{1+51 e^{-0.1 x}}\)
Step 3 :After substituting, we get: \(P = 1.9230769230769231\)
Step 4 :Final Answer: The percentage of the target audience that buys the game without seeing a TV ad is approximately \(\boxed{1.9\%}\).