document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202338>Question 1202338</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At first there were 17 boring beetles. The number of boring beetles doubled every day.\r<BR>\n" );
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document.write( "(a)  Write an equation that describes the number of beetles there would be after n days.\r<BR>\n" );
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document.write( "(b)  Using the equation in (a), determine the number of beetles there would be after 30 days. </SPAN>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "(a)  <font color=red>P = 17*2^n</font><BR>\n" );
document.write( "(b)  <font color=red>18,253,611,008</font> (roughly 18.25 billion)\r<BR>\n" );
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document.write( "Explanation for Part (a)\r<BR>\n" );
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document.write( "One possible exponential equation template is P = a*b^n<BR>\n" );
document.write( "where,<BR>\n" );
document.write( "n = number of days<BR>\n" );
document.write( "P = number of beetles<BR>\n" );
document.write( "a = starting amount<BR>\n" );
document.write( "b = growth rate when b > 1\r<BR>\n" );
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document.write( "In this case,<BR>\n" );
document.write( "a = 17<BR>\n" );
document.write( "b = 2, meaning the population doubles each time n goes up by 1.\r<BR>\n" );
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document.write( "We go from P = a*b^n to <font color=red>P = 17*2^n</font>\r<BR>\n" );
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document.write( "If n = 0, then P = 17<BR>\n" );
document.write( "If n = 1, then P = 34<BR>\n" );
document.write( "If n = 2, then P = 68<BR>\n" );
document.write( "and so on.\r<BR>\n" );
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document.write( "Explanation for Part (b)\r<BR>\n" );
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document.write( "Plug n = 30 into the equation we just found.<BR>\n" );
document.write( "P = 17*2^n<BR>\n" );
document.write( "P = 17*2^30<BR>\n" );
document.write( "P = <font color=red>18,253,611,008</font><BR>\n" );
document.write( "This population count is roughly 18.25 billion.\r<BR>\n" );
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document.write( "I don't know much about beetles, or insects, to know if this population count is realistic or not.<BR>\n" );
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