Final answer:
A hearing aid that increases the sound level by 57.0 dB will amplify the intensity of sounds by a factor of 5.0 × 10^5.
Step-by-step explanation:
If a person wears a hearing aid that increases the sound level by 57.0 dB at all frequencies, we first need to understand the relationship between decibels (dB) and intensity levels. Using the formula for decibel level changes, which is Δ2 = Δ1 × 10^(dB/10), where Δ1 is the original intensity and Δ2 is the final intensity, we can calculate the factor by which the intensity is amplified. To find this factor, we plug in the decibel increase to the formula: factor = 10^(57.0/10).
Calculating this, we find that the intensity of sounds will be amplified by a factor of 5.0 × 10^5. Therefore, a hearing aid that increases the sound level by 57.0 dB will amplify the intensity of sounds by this factor.