document.write( "Question 1189542: An initial population of 30 fish is introduced into a lake. This fish population grows according to a continuous exponential growth model. There are 69 fish in the lake after 12 years.
\n" ); document.write( "(a) Let “t” be the time (in years) since the initial population is introduced, and let y be the number of fish at time t. Write a formula relating y to t.
\n" ); document.write( "Use exact expressions to fill in the missing parts of the formula. Do not use approximations.\r
\n" ); document.write( "\n" ); document.write( "(b) How many fish are there 14 years after the initial population is
\n" ); document.write( "introduced?
\n" ); document.write( "Do not round any intermediate computations, and round your
\n" ); document.write( "answer to the nearest whole number. \n" ); document.write( "

Algebra.Com's Answer #820922 by ikleyn(52806) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "An initial population of 30 fish is introduced into a lake. This fish population grows according to
\n" ); document.write( "a continuous exponential growth model.
\n" ); document.write( "There are 69 fish in the lake after 12 years.
\n" ); document.write( "(a) Let “t” be the time (in years) since the initial population is introduced,
\n" ); document.write( "and let y be the number of fish at time t. Write a formula relating y to t.
\n" ); document.write( "Use exact expressions to fill in the missing parts of the formula. Do not use approximations.
\n" ); document.write( "(b) How many fish are there 14 years after the initial population is
\n" ); document.write( "introduced?
\n" ); document.write( "Do not round any intermediate computations, and round your
\n" ); document.write( "answer to the nearest whole number.
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document.write( "Write an exponential function connecting y and t, as you read the problem\r\n" );
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document.write( "    y = .\r\n" );
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document.write( "You use the factor 30, since 30 fish is the initial population (at t= 0).\r\n" );
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document.write( "The base \"b\" is unknown now; determine it from the given data at t= 12 years\r\n" );
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document.write( "    69 = .\r\n" );
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document.write( "Divide both sides by 30\r\n" );
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document.write( "    = ,   or   2.3 = .\r\n" );
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document.write( "Take logarithm base 10 from both sides\r\n" );
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document.write( "   log(2.3) = 12*log(b)\r\n" );
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document.write( "   log(b) =  = 0.030144\r\n" );
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document.write( "     b    =  = 1.071875.\r\n" );
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document.write( "Thus, your exponential function is fully determined: it is  y = .\r\n" );
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document.write( "Check at t= 12:  y =  = 69  ! PRECISELY CORRECT !\r\n" );
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document.write( "Part (a) is completed.\r\n" );
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document.write( "For part (b), simply substitute t= 14 into the formula and calculate\r\n" );
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document.write( "    y =  = 79.2 = 79 fish  (rounded).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\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( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\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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