The inequality 94 – 3 log2x ≤ 88 describes noise exposure level (in decibels) in terms of the number of hours, x, it takes to reach 100% of a person’s recommended daily noise dose. A manufacturer claims that the noise exposure level in their factory never exceeds 88 decibels. What is the smallest number of hours it would take for a worker in this factory to reach 100% of her daily noise exposure?
At the factory’s maximum level of 88 decibels, set the inequality equal to 88 to find the shortest time: 94 − 3 log₂x = 88. This gives log₂x = 2, so x = 2² = 4 hours. Thus, the smallest time is 4 hours, choice D.
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