gibson:teaching:fall-2013:math445:lab8
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gibson:teaching:fall-2013:math445:lab8 [2013/11/04 17:15] gibson |
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| - | The first column is the [[http://en.wikipedia.org/wiki/Moment_magnitude_scale | moment magnitude]] //M//, and the second column is the number of earthquakes //N// of that magnitude that occur, on average, in a year. The last two entries are estimates, since it's impossible to detect every small earthquake around the world. Data obtained from [[http://www.earthquake.ethz.ch/education/NDK/NDK|Earthquake Statistics and Earthquake Prediction Research]] by Stefan Wiemer, Institute of Geophysics, Zurich. | + | The first column is the [[http://en.wikipedia.org/wiki/Moment_magnitude_scale | moment magnitude]] //M//, and the second column is the number of earthquakes //N// of that magnitude that occur, on average, in a year. The last two entries are estimates, since it's impossible to detect every small earthquake around the world. The data are obtained from [[http://www.earthquake.ethz.ch/education/NDK/NDK|Earthquake Statistics and Earthquake Prediction Research]] by Stefan Wiemer, Institute of Geophysics, Zurich. |
| Using Matlab plotting commands, deduce the form of the functional relationship //N(M)//. Estimate the constants in the relationship by estimating the slope and the //y//-intercept, and then fine-tuning by matching the plot of your estimate against the plot of the data. | Using Matlab plotting commands, deduce the form of the functional relationship //N(M)//. Estimate the constants in the relationship by estimating the slope and the //y//-intercept, and then fine-tuning by matching the plot of your estimate against the plot of the data. | ||
| - | **Problem 2: The distribution of earthquake magnitudes, by energy.** The moment magnitude scale is logarithmic, in that earthquake of magnitude //M+1// releases about 32 times energy than an earthquake of magnitude //M//. The following data | + | **Problem 2: The distribution of earthquake magnitudes, by energy.** The moment magnitude scale is logarithmic, in that an earthquake of magnitude //M+1// releases about 32 times energy than an earthquake of magnitude //M//. The following data |
| set gives the number //N// of earthquakes in a given year of energy //E// measured in Joules. | set gives the number //N// of earthquakes in a given year of energy //E// measured in Joules. | ||
| <code> | <code> | ||
| - | % E N | + | % E N |
| 6e16 2 | 6e16 2 | ||
| 2e15 18 | 2e15 18 | ||
| Line 60: | Line 60: | ||
| in the relation, just as in problem 1. | in the relation, just as in problem 1. | ||
| + | **Problem 3: World population.** The following data set provides the human population //P// of the earth at a given | ||
| + | time //t//, measured in years A.D. | ||
| + | |||
| + | <code> | ||
| + | % t P | ||
| + | 1927 2e09 | ||
| + | 1960 3e09 | ||
| + | 1974 4e09 | ||
| + | 1987 5e09 | ||
| + | 1999 6e09 | ||
| + | 2011 7e09 | ||
| + | </code> | ||
| + | |||
| + | Deduce the form of the functional relation //P(t)// and determine the constants graphically. | ||
| + | |||
| + | Assume that the formula you derived for //P(t)// is valid indefinitely into the future and the past. What year will | ||
| + | the population of the earth reach one trillion? What year were the first humans born? Do you believe these answers? | ||
| + | If not, why not? | ||
gibson/teaching/fall-2013/math445/lab8.1383614103.txt.gz ยท Last modified: 2013/11/04 17:15 by gibson
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