document.write( "Question 926974: An endangered species of fish has a population that is decreasing exponentially (A = aekt). The population 9
\n" ); document.write( "years ago was 1700. Today, only 1000 of the fish are alive. Once the population drops below 100, the situation
\n" ); document.write( "will be irreversible. When will this happen, according to the model? (Round to the nearest whole year.) \n" ); document.write( "

Algebra.Com's Answer #562781 by Fombitz(32388) $\"\"$ $\"About$

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Let 9 years ago be $\"t=0\"$ , then,
\n" ); document.write( " $\"1700=ae%5E%28k%280%29%29=a\"$
\n" ); document.write( "So today, $\"t=9\"$
\n" ); document.write( " $\"1000=1700e%5E%28k%289%29%29\"$
\n" ); document.write( " $\"e%5E%289k%29=10%2F17\"$
\n" ); document.write( " $\"9k=ln%2810%2F17%29\"$
\n" ); document.write( " $\"k=%281%2F9%29ln%2810%2F17%29\"$
\n" ); document.write( "So find $\"t\"$ so that,
\n" ); document.write( " $\"1700e%5E%28kt%29=100\"$
\n" ); document.write( " $\"e%5E%28kt%29=1%2F17\"$
\n" ); document.write( " $\"kt=ln%281%2F17%29\"$
\n" ); document.write( " $\"t=ln%281%2F17%29%2F%28%281%2F9%29ln%2810%2F17%29%29\"$
\n" ); document.write( " $\"t=9%28ln%281%29-ln%2817%29%29%2F%28ln%2810%29-ln%2817%29%29\"$
\n" ); document.write( " $\"highlight%28t=9%28ln%2817%29%29%2F%28ln%2817%29-ln%2810%29%29%29\"$
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