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gibson:teaching:fall-2014:math445:lab3

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 gibson:teaching:fall-2014:math445:lab3 [2014/09/15 12:04]gibson created gibson:teaching:fall-2014:math445:lab3 [2014/09/15 12:05] (current)gibson Both sides previous revision Previous revision 2014/09/15 12:05 gibson 2014/09/15 12:04 gibson created2014/09/15 11:56 gibson removed2014/09/15 11:35 gibson created 2014/09/15 12:05 gibson 2014/09/15 12:04 gibson created2014/09/15 11:56 gibson removed2014/09/15 11:35 gibson created Line 44: Line 44: **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 + ​ + + 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 + ​ + + 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? +