A ski lift is modeled by the function f(x) = (0.2)(–2x 3 + 23x 2 + 25x + 50), where x is the time in seconds. When it comes out of the first stop, it is now climbing toward its highest point from the ground.During which time interval will the ski lift reach a height over 50 feet above the ground?

To find when the lift is above 50 feet, solve f(x) > 50. Dividing by 0.2 gives −2x³ + 23x² + 25x + 50 > 250, or −2x³ + 23x² + 25x − 200 > 0. This expression is positive between its relevant zeros, approximately x = 2.7 and x = 11.8, so the lift is above 50 feet for 2.7 < x < 11.8 seconds. The correct choice is C, “2.7 < x < 11.8.”

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