Why exponents are used in measuring earthquake

A calculator gives a value of [latex]3. One extra point on the Richter scale can mean a lot more shaking! Sound is measured in a logarithmic scale using a unit called a decibel. The formula looks similar to the Richter scale:. In the next example we will find how much more intense the noise from a dishwasher is than the noise from a hot water pump.

The dishwasher noise is how many times more intense than the hot water pump noise? Repeat the same process to find the intensity of the noise for the dishwasher, use d to represent the intensity of the sound of the dishwasher.

To compare d to h, you can divide. Use the laws of exponents to simplify the quotient. Applications of logarithms and exponentials are everywhere in science. We hope the examples here have given you an idea of how useful they can be. Skip to main content. Module Exponential and Logarithmic Equations. Search for:. The formula for the energy in kWh, kiloWatt hours is: where E is the energy, and M is the earthquake magnitude.

Now that you understand the Richter scale, let's try to discover what effect the large earthquake will have on Vancouver. This represents the Alaska earthquake. And this is the Turkey earthquake. Calculate, using exponents, the intensity difference between a 5. Calculate the intensity difference between a 5.

Calculate the intensity difference between an 8. Calculate the energy of a magnitude 8. An earthquake is measured with a wave amplitude times as great as A 0.

What is the magnitude of this earthquake using the Richter scale, to the nearest tenth? Use the Richter scale equation. Substitute this expression in for A. Use a calculator to evaluate the logarithm. The magnitude of this earthquake is 2. A difference of 1 point on the Richter scale equates to a fold difference in the amplitude of the earthquake which is related to the wave strength.

This means that an earthquake that measures 3. In that example, the wave amplitude of the earthquake was times normal. What if it were 10 times that, or 3, times normal? To find the measurement of that size earthquake on the Richter scale, you find log A calculator gives a value of 3. One extra point on the Richter scale can mean a lot more shaking!

Sound is measured in a logarithmic scale using a unit called a decibel. The formula looks similar to the Richter scale:. One hot water pump has a noise rating of 50 decibels. One dishwasher, however, has a noise rating of 62 decibels. The dishwasher noise is how many times more intense than the hot water pump noise? Start by finding the intensity of noise for the hot water pump. Divide the equations by 10 to get the log by itself.

Rewrite the equation as an exponential equation. Multiply by P 0 to get h by itself. Repeat the same process to find the intensity of the noise for the dishwasher. To compare d to h , you can divide. Use the laws of exponents to simplify the quotient.

With decibels, every increase of 10 means the sound is 10 times more intense. An increase of 20 would be 10 times more intense for the first 10, and another 10 times more intense for the second 10—so a sound that is 75 decibels is times more intense than a sound that is 55 decibels! The measure of acidity of a liquid is called the pH of the liquid. The formula for pH is:. Liquids with a low pH down to 0 are more acidic than those with a high pH. Water, which is neutral neither acidic nor alkaline, the opposite of acidic has a pH of 7.

If lime juice has a pH of 1. The concentration of hydrogen ions in lime juice is 0. An earthquake monitoring station measured the amplitude of the waves during a recent tremor. It measured the waves as being , times as large as A 0 , the smallest detectable wave.

How high did this earthquake measure on the Richter scale? An earthquake that measured 1 on the Richter scale would have a wave amplitude of only 10 times greater than normal. To solve this problem, setup the equation as , and solve for R. The correct answer is 5. An earthquake that measured 3 on the Richter scale would have a wave amplitude of 10 3 , or 1, times greater than normal.

To solve this problem, set up the equation as , and solve for R.