document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165543>Question 165543</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is another one that I'm stuck on. This is probably so basic but it's been a VERY long time. Please help! Thanks<BR>\n" );
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document.write( "4. For each of the relationships below, explain whether you think it is best described by a linear function or a non-linear function.  Explain your reasoning thoroughly\r<BR>\n" );
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document.write( "a. A person's height as a function of the person's age (from age 0 to 100)\r<BR>\n" );
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document.write( "b. The probability of getting into a car accident as a function of the speed at which you drive\r<BR>\n" );
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document.write( "c. The time it takes you to get to work as a function the speed at which you drive </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122015 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=122015\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. A person's height as a function of the person's age (from age 0 to 100)<BR>\n" );
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document.write( "i would say non-linear.<BR>\n" );
document.write( "there is a large growth spurt in the early years and then it tapers off to about nothing for a long period of time.<BR>\n" );
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document.write( "b. The probability of getting into a car accident as a function of the speed at which you drive.<BR>\n" );
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document.write( "again i would say non-linear.<BR>\n" );
document.write( "there does not appear to be a straight line correlation.<BR>\n" );
document.write( "some studies show it as exponential.<BR>\n" );
document.write( "there are also too many variables involved to isolate speed as a directly causative factor unless it's far in excess of what's considered reasonable. <BR>\n" );
document.write( "if you go to extremes, then it's clear that there's a positive correlation and i would estimate exponential increases in the probability of having an accident the faster you go with small increases early on but much bigger as you get up there.<BR>\n" );
document.write( "example would be going down a city street.<BR>\n" );
document.write( "at 25 p(a) is very small.<BR>\n" );
document.write( "at 30 still small.<BR>\n" );
document.write( "at 35 still small.<BR>\n" );
document.write( "at 40 still small but getting bigger.<BR>\n" );
document.write( "at 50 bigger.<BR>\n" );
document.write( "at 60 much bigger.<BR>\n" );
document.write( "it goes up astronomically from there.<BR>\n" );
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document.write( "c. The time it takes you to get to work as a function the speed at which you drive<BR>\n" );
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document.write( "this is also non-linear.<BR>\n" );
document.write( "it's more of a ratio, i.e. time to get there = distance / speed.<BR>\n" );
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document.write( "you can use straight lines to provide regression analysis, but a curve fitting program that finds an equation that fits the data would be more suitable.<BR>\n" );
document.write( "an online version of one is at this internet address.<BR>\n" );
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document.write( "http://people.hofstra.edu/Stefan_Waner/RealWorld/newgraph/regressionframes.html<BR>\n" );
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document.write( "if you plot some points you can see which of the curves fits best.  none of them are perfect, except for the last one that you asked (speed versus time to get to work, the equation of y = ax^b seemed to work best.  in my test data the equation worked out to be y = 100x^-1 which translated to y = 100/x.  where y was the time to get to work, 100 was the miles to get to work (a), and x was the speed. </SPAN>\n" );
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