document.write( "Question 1192399: Not sure what to do.\r
\n" ); document.write( "\n" ); document.write( "The following table represents the number of koala bears alive since the year 2000. Write a function for the koala bear population, P(t), as a function of t, the time in years since 2000.\r
\n" ); document.write( "\n" ); document.write( "1(time since 2000)-------------------P(population of koala bears)
\n" ); document.write( " 0 --------------------------- 100,000
\n" ); document.write( " 1---------------------------- 93,500
\n" ); document.write( " 2---------------------------- 87,423
\n" ); document.write( " 21--------------------------- 24,381
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Algebra.Com's Answer #824291 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "Not sure what to do.
\n" ); document.write( "The following table represents the number of koala bears alive since the year 2000.
\n" ); document.write( "Write a function for the koala bear population, P(t), as a function of t, the time in years since 2000.
\n" ); document.write( "1(time since 2000)-------------------P(population of koala bears)
\n" ); document.write( "0 --------------------------- 100,000
\n" ); document.write( "1---------------------------- 93,500
\n" ); document.write( "2---------------------------- 87,423
\n" ); document.write( "21--------------------------- 24,381
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Looking into the table, we see that the number of koala bears k(x) is decreasing with years.\r\n" );
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document.write( "It is naturally to assume that we have decaying exponential function.\r\n" );
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document.write( "To check it, calculate the ratios for consecutive years\r\n" );
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document.write( "     =  = 0.935,   =  = 0.935.\r\n" );
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document.write( "Thus we see that we have a geometric progression with the common ratio r = 0.935.\r\n" );
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document.write( "To check it, calculate k(21) using the formula for geometric progression\r\n" );
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document.write( "    k(21) =  = 24381.\r\n" );
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document.write( "Comparing it with the last value in the Table, you see that you have every reason to use the formula \r\n" );
document.write( "of geometric progression\r\n" );
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document.write( "    k(x) =      (1)\r\n" );
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document.write( "to calculate the population of koal bears k(x) in the entire interval 0 <= x <= 21,\r\n" );
document.write( "where x denotes the years since 2000.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Exponential functions of the type (1) are typical functions to predict population growth/decay.\r
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\n" ); document.write( "\n" ); document.write( "---------------\r
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\n" ); document.write( "\n" ); document.write( "Solved and explained.\r
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\n" ); document.write( "\n" ); document.write( "If you want to see many other similar and different solved problems on population growth, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Population growth problems \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Logarithms\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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