gibson:teaching:fall-2014:math445:lab3

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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.txt · Last modified: 2014/09/15 12:05 by gibson