document.write( "Question 1163016: A plant grows 1.67 cm in its first week. Each week it grows by 2% more
\n" ); document.write( "than it did the week before. By how much does it grow in twenty weeks,
\n" ); document.write( "including the first week? \n" ); document.write( "
Algebra.Com's Answer #786957 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
this looks like a geometric progression.
\n" ); document.write( "it grows by 1.67 the first week.
\n" ); document.write( "it grows by 1.67 * 1.02 the second week.
\n" ); document.write( "this continues until the 20th week.
\n" ); document.write( "this sound like the sum of a geometric progression.
\n" ); document.write( "the formula for that is Sn = A1 * (1 - r^n) / (1 - r)
\n" ); document.write( "A1 = 1.67
\n" ); document.write( "r = 1.02
\n" ); document.write( "n = 20
\n" ); document.write( "S20 = 1.67 * (1 - 1.02^20) / (1 - 1.02) = 1.67 * -.485947396 / -.02 = 40.57660756.
\n" ); document.write( "to see the progression week by week, view the following.
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\n" ); document.write( "\n" ); document.write( "you can see that the growth in the first week was 1.67 centimeters fpr a total of 1.67 centimeters; the growth in the second week was 1.7034 centimeters for a total of 3.3734 centimeters; the growth in the third week was 1.737468 centimeters for a total of 5.110868 centimeters; etc.....\r
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\n" ); document.write( "\n" ); document.write( "after the first week, each week's growth was 2% higher than the growth in the week before.
\n" ); document.write( "1.67 * 1.02 = 1.7034; 1.7034 * 1.02 = 1.737468; etc.....\r
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\n" ); document.write( "\n" ); document.write( "your solution is a total growth of 40.57660756 centimeters in 20 weeks.\r
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