document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129564>Question 129564</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the following is a growth curve?<BR>\n" );
document.write( "a)y=0.6^x<BR>\n" );
document.write( "b)y=(2/3)^-x<BR>\n" );
document.write( "c)y=3.5^-x<BR>\n" );
document.write( "d)y=2(1/3)^x<BR>\n" );
document.write( "I think the answer is (d). Can someone please confirm??? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94604 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=94604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The correct answer is answer b. <BR>\n" );
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document.write( "Let's look at a quick way to tell. <BR>\n" );
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document.write( "First let's look at answer a). If x is zero, then y = (0.6)^0 and when you raise a number to<BR>\n" );
document.write( "the zero power, the answer is 1. What happens if we next let x = 1? When x = 1 then the<BR>\n" );
document.write( "equation for y is y = (0.6)^1 = 0.6. Right away we can see that as x increased from 0 to 1<BR>\n" );
document.write( "that y decreased from 1 to 0.6 ... this is a decreasing graph and not a growth curve.<BR>\n" );
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document.write( "Next let's look at answer c). If x is 0 then y = (3.5)^-0 = (3.5)^0 = 1. Next let's let x = 1.<BR>\n" );
document.write( "Then y becomes y = (3.5)^(-1) = 1/(3.5) = 0.2857. Therefore, as x increased from 0 to 1, the <BR>\n" );
document.write( "value of y decreased from 1 to 0.2857<BR>\n" );
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document.write( "Then let's look at answer d). If x is 0 then y = 2*(1/3)^0 = 2*1 = 2. Now let x = 1 and<BR>\n" );
document.write( "the value of y becomes y = 2*(1/3)^1 = 2*(1/3) = 2/3. So when x increased from 0 to 1, the<BR>\n" );
document.write( "corresponding value of y decreased from 2 to 2/3. This is not a growth curve.<BR>\n" );
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document.write( "Finally let's look at answer b). When x equals 0 then y = (2/3)^(-0) = (2/3)^0 = 1. Now let x<BR>\n" );
document.write( "grow to 1 and the corresponding value of y becomes (2/3)^(-1) = 1/(2/3)^1 = 1/(2/3) = 3/2<BR>\n" );
document.write( "So when x goes from 0 to 1, y increased from 1 to 3/2. This increasing y with increasing x<BR>\n" );
document.write( "represents a growth curve. Therefore, b) is the correct answer.<BR>\n" );
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document.write( "Hope this quick method helps you to see how you can determine if a curve is a growth curve.<BR>\n" );
document.write( "You can try other values of x in each answer ... for example, let x = 2 and you should get<BR>\n" );
document.write( "the same result ... only in answer b) will the value of y increase as x goes from 1 to 2.<BR>\n" );
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