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gibson:teaching:fall-2014:math445:exam2samplesolns [2014/10/29 12:28]
gibson created
gibson:teaching:fall-2014:math445:exam2samplesolns [2014/10/29 12:33] (current)
gibson
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 8. What is y as a function of x?  8. What is y as a function of x? 
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 +{{:​gibson:​teaching:​fall-2014:​math445:​exam2sampleplot1.png?​nolink&​300|}}
  
 The log10 y versus x plot is a straight line, so the form of the equation is The log10 y versus x plot is a straight line, so the form of the equation is
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 y drops from just above 10^5 to just above 10^-5 as x goes from -2 to 3.  y drops from just above 10^5 to just above 10^-5 as x goes from -2 to 3. 
 Equivalently,​ log10 y drops from just above 5 to just above -5 as x goes  Equivalently,​ log10 y drops from just above 5 to just above -5 as x goes 
-from -2 to 3. Therefore the slope m of the line log10 y = mx + b around ​+from -2 to 3. Therefore the slope m of the line log10 y = mx + b is around ​
 m = rise/run = -10/5 = -2. At x=0, y is about 10^1. Plugging that into  m = rise/run = -10/5 = -2. At x=0, y is about 10^1. Plugging that into 
 y = c 10^(-2x) gives c=10. Therefore the relation between y and x is  y = c 10^(-2x) gives c=10. Therefore the relation between y and x is 
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 9. What is y as a function of x?  9. What is y as a function of x? 
  
 +{{:​gibson:​teaching:​fall-2014:​math445:​exam2sampleplot2.png?​nolink&​300|}}
  
 The log10 y versus log10 x plot is a straight line, so the form of the equation ​ The log10 y versus log10 x plot is a straight line, so the form of the equation ​
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 log10 y goes from -6 to 10 as log10 x goes from -2 to 6. So the line log10 y = m log10 x + b log10 y goes from -6 to 10 as log10 x goes from -2 to 6. So the line log10 y = m log10 x + b
 has slope of roughly m = 16/8 = 2. At x=10^6, y=10^10. Plugging that into y = c x^2 gives  has slope of roughly m = 16/8 = 2. At x=10^6, y=10^10. Plugging that into y = c x^2 gives 
-c = 10^-2. Therefore the relation between y and x is y = 0.01 x^2+c = 10^-2. Therefore the relation between y and x is roughly ​y = 0.01 x^2
gibson/teaching/fall-2014/math445/exam2samplesolns.txt ยท Last modified: 2014/10/29 12:33 by gibson