document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168785>Question 1168785</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The annual income of Ana in 2011 was Php 450,000. From 2011 to 2015, her income increased by 30%. What was Ana's total income from 2011 to 2015?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793402 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=793402\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if it grew by the same percent increase each year, then the average amount that it grew each year would be 1.3 ^ (1/(2015-2011) = 1.3 ^ (1/4) = by a factor of 1.067789972.<BR>\n" );
document.write( "take 1 away and multiply by 100 to get 6.7789972 percent increase each year.<BR>\n" );
document.write( "rounded to the nearest dollar, her income each year from 2011 to 2015 would be:<BR>\n" );
document.write( "2011 = 450,000<BR>\n" );
document.write( "2012 = 480,505<BR>\n" );
document.write( "2013 = 513,078<BR>\n" );
document.write( "2014 = 547,860<BR>\n" );
document.write( "2015 = 585,000\r<BR>\n" );
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document.write( "if it grew by the amount each year, then the average amount that it grew each year would (585,000 - 450,000) / 4 = 33,750 each year.<BR>\n" );
document.write( "her income each year from 2011 to 2015 would be:<BR>\n" );
document.write( "2011 = 450,000<BR>\n" );
document.write( "2012 = 483,750<BR>\n" );
document.write( "2013 = 517,500<BR>\n" );
document.write( "2014 = 551,250<BR>\n" );
document.write( "2015 = 585,000\r<BR>\n" );
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document.write( "the first growth was exponential growth.<BR>\n" );
document.write( "it was the same percent increase each year.\r<BR>\n" );
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document.write( "the second growth was straight line growth rate.<BR>\n" );
document.write( "it was the same amount each year.\r<BR>\n" );
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document.write( "the exponential growth multiplies by the same growth factor each year.<BR>\n" );
document.write( "the amount of growth each year increases, but the percent growth remains the same.\r<BR>\n" );
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document.write( "the straight line growth adds the same growth each factor.<BR>\n" );
document.write( "the percent growth decreases each year, but the amount of growth remains the same.\r<BR>\n" );
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document.write( "the percent growth equation is y = a * b^x<BR>\n" );
document.write( "in your problem, a was 450,000 and b was 1.3 for every 4 years and b was 1.067789972 for each year.\r<BR>\n" );
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document.write( "to find the yearly growth rate, you had to take the 4th root of the 4 year growth rate.<BR>\n" );
document.write( "1.3 ^ (1/4) = 1.067789972.\r<BR>\n" );
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document.write( "the straight line growth used the equation of y = m * x + b<BR>\n" );
document.write( "m was the slope, or the average increase each year.<BR>\n" );
document.write( "b was the y-intercept, which is the value of y when the value of x is 0.<BR>\n" );
document.write( "in your problem the equation was y = 33,750 * x + 450,000<BR>\n" );
document.write( "the slope was 33,750 and the y-intercept was 450,000.\r<BR>\n" );
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document.write( "the end points of the straight line growth and the exponential growth were the same, at least for the initial 4 year period.\r<BR>\n" );
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document.write( "after that, the exponential growth takes off and the straight line growth remains the same.\r<BR>\n" );
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document.write( "not sure which one you needed, so i gave you both.\r<BR>\n" );
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document.write( "let me know if you have any questions about this.\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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