gibson:teaching:fall-2014:math445:lab3
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gibson:teaching:fall-2014:math445:lab3 [2014/09/15 12:04] gibson created |
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| **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 | **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 | ||
| Line 51: | Line 50: | ||
| 6e13 120 | 6e13 120 | ||
| 2e12 800 | 2e12 800 | ||
| - | 6e10 | + | 6e10 6200 |
| + | 2e09 49000 | ||
| + | 6e07 365000 | ||
| + | 1e06 2920000 | ||
| + | </code> | ||
| + | |||
| + | Deduce the form of the functional relation //E(N)// using Matlab plotting, then estimate and fine-tune the constants | ||
| + | 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-2014/math445/lab3.1410807891.txt.gz · Last modified: 2014/09/15 12:04 by gibson
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