Final answer:
The sound intensity of the boiler shop is 10⁶ (one million) times greater than that of the quiet library. Therefore, the correct answer is a) 10^6.
Step-by-step explanation:
The student has asked how many times greater the sound intensity of the boiler shop is compared to the library if the library's sound intensity level is 40 dB and the boiler shop's is 100 dB. To calculate this, we use the fact that each 10 dB difference in sound intensity level corresponds to a factor of 10 in intensity. Thus, a 100 dB sound compared with a 40 dB sound is 60 dB greater, or six factors of 10 (106 times) as intense.
The sound intensity level is measured in decibels (dB), and each factor of 10 in intensity corresponds to 10 dB. In this case, the sound intensity level in the quiet library is 40 dB, and in the boiler shop, it is 100 dB. To determine how many times greater the sound intensity of the shop is compared to the library, we need to find the difference in dB.
The difference in dB between the two sound intensity levels is 100 dB - 40 dB = 60 dB. Since each factor of 10 in intensity corresponds to 10 dB, a difference of 60 dB means the sound intensity of the shop is 10^6 (1,000,000) times greater than that of the library.
Therefore, the correct answer is a) 10^6.