document.write( "Question 1136573: Recursive equations can be very handy for modeling complicated situations for which explicit equations would be hard to interpret. As an example, consider a lake in which 2000 fish currently reside. The fish population grows by 10% each year, but every year 100 fish are harvested from the lake by people fishing.
\n" ); document.write( "a. Write a recursive equation for the number of fish in the lake after n years.
\n" ); document.write( "b. Calculate the population after 1 and 2 years. Does the population appear to be increasing or decreasing?
\n" ); document.write( "c. What is the maximum number of fish that could be harvested each year without causing the fish population to decrease in the long run? \n" ); document.write( "

Algebra.Com's Answer #754351 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "I interpret this problem in this way:\r
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document.write( "    Each year the fish population increase by 10%, but on tDecember, 31, each year a fisherman comes and harvests 100 fish at once.\r\n" );
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document.write( "(a)   = ,   = 2000,   n = 1, 2, 3, . . . \r\n" );
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document.write( "(b)   = 1.1*2000 - 100 = 2100;\r\n" );
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document.write( "      = 1.1*2100 - 100 = 2210.\r\n" );
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document.write( "(c)  This maximum value is exactly 10% of 2000, which is 200 fish.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answered and solved.\r
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\n" ); document.write( "\n" ); document.write( "There is another area of human activity, where processes go precisely in accordance with this scheme.\r
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\n" ); document.write( "\n" ); document.write( "It is withdrawing of certain amount of money at the end of each year from a banking account compounded annually.\r
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\n" ); document.write( "\n" ); document.write( "This area is completely covered by mathematical formulas.\r
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\n" ); document.write( "\n" ); document.write( "You can read about it and about adjacent issues from the lessons\r
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\n" ); document.write( "\n" ); document.write( "    - Ordinary Annuity saving plans and geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Annuity Due saving plans and geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on Ordinary Annuity saving plans \r
\n" ); document.write( "\n" ); document.write( "    - Withdrawing a certain amount of money periodically from a compounded saving account (*)\r
\n" ); document.write( "\n" ); document.write( "    - Miscellaneous problems on retirement plans \r
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\n" ); document.write( "\n" ); document.write( "in this site, and especially from the lesson marked (*) in the list as the most relevant to the given problem.\r
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