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gibson:teaching:fall-2014:math445:lab3 [2014/09/15 12:04]
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gibson:teaching:fall-2014:math445:lab3 [2014/09/15 12:05] (current)
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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