In the afternoon, the decibel level of a busy freeway is 89 dB with 90 cars passing a given point every minute. Late at night, the traffic flow is only 5 cars per minute. What is the late-night decibel level?Select one:a.76 dBb.​9 dBc.176 dBd.89 dBe.205 dB

The decibel level is a logarithmic measure of the intensity of a sound. In this case, the intensity of the sound is directly proportional to the number of cars passing a given point per minute.

Given that the decibel level is 89 dB when 90 cars pass a given point every minute, we can set up a proportion to find the decibel level when only 5 cars pass the same point every minute.

Let's denote the unknown decibel level as X. The proportion can be set up as follows:

90 cars/minute : 89 dB = 5 cars/minute : X dB

Solving for X gives:

X = (5 cars/minute * 89 dB) / 90 cars/minute

X = 4.94 dB

However, decibel is a logarithmic unit, so we can't simply scale it linearly. Therefore, the calculation above is incorrect.

The correct way to approach this problem is to understand that every halving of the intensity of a sound corresponds to a reduction of about 3 dB.

If we go from 90 cars to 45 cars, that's a halving, so we reduce by 3 dB to get 86 dB.

If we go from 45 cars to 22.5 cars, that's another halving, so we reduce by another 3 dB to get 83 dB.

We can see that reducing the number of cars to 5 won't get us to a halving again, so the late-night decibel level will be somewhere above 83 dB but below 86 dB.

None of the options a. 76 dB, b. 9 dB, c. 176 dB, d. 89 dB, e. 205 dB match this range.

Therefore, it seems like there might be a mistake in the question or the answer choices.

The decibel level is not directly proportional to the number of cars. It's a logarithmic scale. Therefore, we can't calculate the late-night decibel level just based on the decrease in the number of cars. We would need more information about how the noise level changes with the number of cars. So, without additional information, we can't determine the late-night decibel level from the options given.