The amount of water leaking from a water tank can be modeled with the function f(x) = −x3 − 10x2 − x + 120, where x measures the number of minutes since the leak began and f(x) measures the volume of the tank. During what time period is there water in the tank?

Factor the volume function: f(x) = −(x − 3)(x + 5)(x + 8), so its zeros are x = −8, −5, and 3. Since x is minutes since the leak began, only x ≥ 0 is relevant. The volume is positive from x = 0 up to, but not including, x = 3; at 3 minutes the tank is empty. Therefore, the answer is (0, 3), choice C.

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