Final answer:
To determine the woman's hearing loss in dB, given the amplification needed, we apply the decibel calculation formula. After substituting the given amplification factor into the formula, we find that her hearing loss is approximately 127 dB, which is not one of the options provided in the question.
Step-by-step explanation:
If a woman needs an amplification of 5.0 × 10¹² times the threshold intensity to hear at all frequencies, her overall hearing loss in dB can be calculated using the formula for decibel levels:
L = 10 × log(I / I0)
Where L is the level in decibels, I is the intensity of sound, and I0 is the threshold intensity of hearing. In this case, I/I0 is 5.0 × 10¹². Plugging in the numbers, we get:
L = 10 × log(5.0 × 10¹²)
L ≈ 10 × (12 + log(5))
L ≈ 10 × (12 + 0.6990)
L ≈ 10 × 12.6990
L ≈ 126.99 dB
This implies that the woman's hearing loss would be approximately 127 dB when rounded to the nearest decibel.