PLEASE HELP-DUE APRIL 5TH, 2011!!!!
EARTHQUAKES an earthquake rated at 3.5 on the Richter scale is felt by many people, and an earthquake rated at 4.5 may cause local damage. The Richter scale magnitude reading m is given by m = log (base 10) x, where x represents the amplitude of the seismic wave causing ground motion. How many times greater is the amplitude of an earthquake that measures 4.5 on the Richter scale than one that measures 3.5?
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To find out how many times greater the amplitude of an earthquake that measures 4.5 on the Richter scale is compared to one that measures 3.5, we need to compare their amplitudes.
Using the formula m = log (base 10) x, where m is the Richter scale magnitude and x represents the amplitude of the seismic wave, we can rearrange the formula to solve for x:
x = 10^m
For an earthquake measuring 4.5 on the Richter scale, the amplitude can be calculated as:
x1 = 10^4.5
And for an earthquake measuring 3.5 on the Richter scale, the amplitude can be calculated as:
x2 = 10^3.5
To find how many times greater x1 is compared to x2, we divide x1 by x2:
(x1/x2) = (10^4.5) / (10^3.5)
To simplify this division, we can subtract the exponents:
(x1/x2) = 10^(4.5 - 3.5)
(x1/x2) = 10^1
Therefore, the amplitude of an earthquake that measures 4.5 on the Richter scale is 10 times greater than one that measures 3.5.
To find out how many times greater the amplitude of an earthquake that measures 4.5 on the Richter scale is compared to one that measures 3.5, we need to calculate the difference in amplitudes.
According to the Richter scale equation, m = log (base 10) x, where m represents the magnitude and x represents the amplitude. We can rewrite this equation to solve for x:
x = 10^m
For an earthquake measuring 3.5 on the Richter scale, we have:
x(3.5) = 10^3.5
And for an earthquake measuring 4.5 on the Richter scale, we have:
x(4.5) = 10^4.5
To find the ratio of the amplitude, divide the amplitude of the earthquake measuring 4.5 on the Richter scale by that of the earthquake measuring 3.5 on the Richter scale:
x(4.5) / x(3.5) = (10^4.5) / (10^3.5)
To simplify the equation, we can use the properties of exponents, specifically the property (a^b) / (a^c) = a^(b - c):
x(4.5) / x(3.5) = 10^(4.5 - 3.5) = 10^1 = 10
Therefore, the amplitude of an earthquake that measures 4.5 on the Richter scale is 10 times greater than that of an earthquake measuring 3.5 on the Richter scale.