gibson:teaching:fall-2014:math445:exam2samplesolns

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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