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

Answer 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

brainly.com/question/15978376

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