A marine biologist is testing a new under water probe. The probe is catapulted from the ship into the air, descends under water to a predetermined depth, and then returns to the surface where it can be collected. The function that models the probe’s path is f(x) = 15t2 – 195t + 450, where t is time measured in seconds. The probe enters the water at 3 seconds. How long is the probe under water?

Answer 1

f(t) = 15(t-3)(t-10)

Clearly f(t) < 0 on the interval (3,10)