Algebra.Com's Answer #842225 by ikleyn(52814)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
.
\n" );
document.write( "You and your parents are working on a scrap book representing your family tree.
\n" );
document.write( "You would like to include one page for each ancestor, and your parents want you to include a page or yourself.
\n" );
document.write( "(a) How many generations can you include with keeping it fewer than 300 pages,
\n" );
document.write( "(b) how many pages would you need to 12 generations of ancestors,
\n" );
document.write( "(c) and assuming that one generation spans about 30 years, what s the earliest year that will appear in the book?
\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "\r\n" );
document.write( "In this family tree, you need 1 page for yourself; 2 pages for your parents,\r\n" );
document.write( "4 pages for your grandparents, and so on:  pages for all ancestors of the n-th generation up from you.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, for all ancestors <= N generations up from you (including you) you need\r\n" );
document.write( "\r\n" );
document.write( " 1 + 2 + 4 + 8 + . . . +  =  pages in your book.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(a) Having fever than 300 pages, you can place the info about N generations up from you, where\r\n" );
document.write( "\r\n" );
document.write( " < 300, of  <= 300, N+1 <=  ~ 8.22.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " So, to evaluate the integer number N of generations up, you need take N ~ 8.22-1 = 7.22\r\n" );
document.write( " and round it to the closest lesser integer, which is 7.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " Thus the ANSWER to question (a) is N = 7, or seven generations up from you, \r\n" );
document.write( " counting you as the 0-th generation.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " Below is the Table, counting pages \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " n the number of accessors the number of ancestors \r\n" );
document.write( " in the n-th generation in all n generations\r\n" );
document.write( " up from you including you up from you including you\r\n" );
document.write( " (same as the number of pages)\r\n" );
document.write( " ----------------------------------------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( " 0 (you) 1 1 \r\n" );
document.write( "\r\n" );
document.write( " 1 2 1+2 = 3\r\n" );
document.write( "\r\n" );
document.write( " 2 4 1+2+4 = 7\r\n" );
document.write( "\r\n" );
document.write( " 3 8 7+8 = 15\r\n" );
document.write( "\r\n" );
document.write( " 4 16 15+16 = 31\r\n" );
document.write( "\r\n" );
document.write( " 5 32 31+32 = 63\r\n" );
document.write( "\r\n" );
document.write( " 6 64 63+64 = 127\r\n" );
document.write( "\r\n" );
document.write( " 7 128 127+128 = 255\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " Here, at the generation 7, you must stop, because you have no more than 299 pages. \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(b) For 12 generations of ancestors, you need  = 8191 pages (including you).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(c) To answer (c), I should know exactly, for what number of generations this question does relate,\r\n" );
document.write( " which is not given in the question.\r\n" );
document.write( " \r
\n" );
document.write( "\n" );
document.write( "Solved.\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( " \n" );
document.write( " |