When an earthquake is reported on the news, you are typically given the magnitude. However, when...

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When an earthquake is reported on the news, you are typically given the magnitude. However, when we want to get an idea of how strong an earthquake is, we humans need to compare it to something we've experienced such as images from previous earthquakes or the feeling we remembered experiencing an earthquake. The variable we are interested in is the intensity. As you may notice in the charts above, in the intensity chart, the numbers are increasing exponentially. By taking the log(100), we get 2 and Log(1000) = 3 in other words, by taking the log of a number, we get a much more manageable number to use in conversations. However, the caveat is that if we give the magnitude in a conversation, we need to transform it back to the intensity to make sense of the numbers. Let's say the news reports an earthquake of magnitude of 6.2. We can work backwards to determine the intensity, In addition, you're ben though an earthquake that was a 4.2 so you want to know how many times stronger it felt. Intensity -5 y 10 5 0 5 Log (Intensity) = Magnitude -5 y 10 5 5 So a 6.2 Earthquake would feel 1000 times stronger than a 3.2 magnitude earthquake. Although there are other formulas on the internet that we can use to calculate this final answer. consider the relationship between exponents and logarithms and see if you understand why those formulas exist. II. Now it's your turn. 1) Sketch and label the graphs below (you do not need to be precise) x Decibel (dB) AO B 20 C 40 D 60 E 80 F 100 x Intensity A1 B 10 C 100 D 1000 E 10000 F 100,000 2) What is the relationship between the y-values of the amplitude and decibei? Notice that the log I does not exactly equal the dB so you'll need to solve for x first. 3) How much more intense is a whisper measuring 45 dB compared to rock concert measuring 120 dB? III. Other logarithmic relationships Look online and find one other logarithmic relationship and answer the following questions like you did in part I and II. 1. Sketch and label the graphs below (you do not need to be precise) 2. Determine if any adjustments to the formula need to be made. 3. How much more intense is a. 4. Look online and give another example. compared to When an earthquake is reported on the news, you are typically given the magnitude. However, when we want to get an idea of how strong an earthquake is, we humans need to compare it to something we've experienced such as images from previous earthquakes or the feeling we remembered experiencing an earthquake. The variable we are interested in is the intensity. As you may notice in the charts above, in the intensity chart, the numbers are increasing exponentially. By taking the log(100), we get 2 and Log(1000) = 3 in other words, by taking the log of a number, we get a much more manageable number to use in conversations. However, the caveat is that if we give the magnitude in a conversation, we need to transform it back to the intensity to make sense of the numbers. Let's say the news reports an earthquake of magnitude of 6.2. We can work backwards to determine the intensity, In addition, you're ben though an earthquake that was a 4.2 so you want to know how many times stronger it felt. Intensity -5 y 10 5 0 5 Log (Intensity) = Magnitude -5 y 10 5 5 So a 6.2 Earthquake would feel 1000 times stronger than a 3.2 magnitude earthquake. Although there are other formulas on the internet that we can use to calculate this final answer. consider the relationship between exponents and logarithms and see if you understand why those formulas exist. II. Now it's your turn. 1) Sketch and label the graphs below (you do not need to be precise) x Decibel (dB) AO B 20 C 40 D 60 E 80 F 100 x Intensity A1 B 10 C 100 D 1000 E 10000 F 100,000 2) What is the relationship between the y-values of the amplitude and decibei? Notice that the log I does not exactly equal the dB so you'll need to solve for x first. 3) How much more intense is a whisper measuring 45 dB compared to rock concert measuring 120 dB? III. Other logarithmic relationships Look online and find one other logarithmic relationship and answer the following questions like you did in part I and II. 1. Sketch and label the graphs below (you do not need to be precise) 2. Determine if any adjustments to the formula need to be made. 3. How much more intense is a. 4. Look online and give another example. compared to

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The relationship between exponents and logarithms is based on the fact that logarithms are the inverse operations of exponentiation Lets go through the relationship and understand why the formulas exi... View the full answer