Question

A certain hallway in a crowded nightclub has a unique sound property. Every 2 feet closer to the stage you walk, the sound intensity (dB) doubles. If the threshold for pain is 127 dB, and the starting sound level is 2 dB, about how many feet down the hallway can you go until you start to feel pain

1. The number of feet down the hallway where you go until you start to feel pain is 14 feet.

### What is geometric progression GP?

A sort of sequence known as geometric progression (GP) is one in which each following phrase is created by multiplying every preceding term by such a fixed number, or “common ratio.”
The general form of GP is
a, ar, ar², ar³ … arⁿ⁻¹
where, a is the initial term.
r is the common ratio.
According to the question,
The initial term is; a = 2.
The common ratio r = 2.
The threshold value beyond which  person start feeling pain is 127.
Thus, last term; arⁿ⁻¹ = 128 (1 feet beyond 127 person start feeling pain)
Last second value is arⁿ⁻².
As, the common ratio is same in GP.
Thus,  arⁿ⁻¹ / arⁿ⁻² = ar/a
==> 128/arⁿ⁻² = r
==> 128/arⁿ⁻² = 2
==> 2×2ⁿ⁻² = 64
==> 2ⁿ⁻² = 32
==> n = 7
As, i step is of 2 feet, the total steps taken by the person is 2×7 = 14.
Therefore, the total number of steps beyond which person will feel pain is 14.
To know more about the geometric progression, here
#SPJ4