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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 2014/10/29 12:33 gibson 2014/10/29 12:28 gibson created 2014/10/29 12:33 gibson 2014/10/29 12:28 gibson created Line 118: Line 118: 8. What is y as a function of x? 8. What is y as a function of x? + + {{:​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 Line 124: Line 126: 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 Line 132: Line 134: 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 ​ Line 141: Line 144: 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