document.write( "Question 1207489: An insect population grows every day. The growth rate of the number of insects per day is described by the function i(t) = 100. e^0.2t, where t is the number of days counted from a certain moment. Calculate using ICT but NOTE the calculation that you make with ICT!
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document.write( "a) By how many insects has the population grown during the first ten days?
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document.write( "• Calculation:
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document.write( "Answer:
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document.write( "b) By how many insects has the population grown on the eleventh day?
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document.write( "• Calculation:
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document.write( "Answer:
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Algebra.Com's Answer #845398 by Theo(13342)![]() ![]() You can put this solution on YOUR website! your equation appears to be:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "f(t) = 100 * e ^ (.2 * t).\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "when t = 0, the formula becomes f(t) = 100 * e ^ (0).\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "since e ^ (.2 * 0) = 1, then f(t) = 100 when t = 0.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "it appears that, at t = 0, you have 100 insects.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "when t = 10, you have 100 * e ^ (.2 * 10) = 738.9056099 insects.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "that is 638.9056099 more than when you started.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "that's your growth.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "when t = 11, you will have 738.9056099 * e ^ (.2 * (11 - 10) = 738.9056099 * e ^ (.2 * 1) = 902.5013499 insects.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "your growth is 902.5013499 minus 738.9056099 = 163.59574 insects in 1 additional day from day 10 to day 11.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "this equation can be graphed.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "it looks like this.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " ![]() \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "since the number of insects has to be an integer, then you need to round your results.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "your choice is to round your final results only, or to round all intermediate results as well.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "an argument can be made that you would need to round all intermediate results, since the number of insects has to be an integer every time you take a tally.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "the spreadsheet below shows the results of not rounding, rounding after all calculations have been performed, rounding down only, rounding up only, or rounding to the nearest integer.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "you just need to decide which rounding option is appropriate for the problem you are working n.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " ![]() \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |