Step 1 :The problem describes an inverse variation. Inverse variation can be modeled by the equation \(y = k/x\), where \(k\) is the constant of variation. In this case, the number of videos sold (\(y\)) varies inversely with the price per video (\(x\)).
Step 2 :We can find the constant of variation by plugging in the given values into the equation: \(610 = k/15.70\).
Step 3 :Solving for \(k\), we get \(k = 9577.0\).
Step 4 :We can use this constant of variation to predict the number of videos sold when the price is $13.60. We substitute \(k = 9577.0\) and \(x = 13.60\) into the equation \(y = k/x\).
Step 5 :Solving for \(y\), we get \(y = 704\).
Step 6 :Final Answer: The manager expects to sell \(\boxed{704}\) videos if he lowers the price to $13.60.