document.write( "Question 973855: Please Help!!!
\n" ); document.write( "The population P of fish, in thousands, in a certain pond at time t years is modeled by the function P(t)= 1/ (1+[(1/P*)-1]e^-rt), where P* is the population at the time t=0 and r is the growth rate of the population. If P(1)=5, which of the following is equivalent to r?
\n" ); document.write( "A) ln(5)/P*
\n" ); document.write( "B) ln(5)/ln(1/P*)
\n" ); document.write( "C) In(4P*/5P*)
\n" ); document.write( "D) ln(4/5P*)
\n" ); document.write( "E) ln(5(P*-1)/4P*) \n" ); document.write( "

Algebra.Com's Answer #595923 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"P%28t%29\"$ = $\"+1%2F%281%2B%281%2FP%5E%22%2A%22-1%29e%5E%28-rt%29%29\"$ so $\"P%281%29\"$ = $\"+1%2F%281%2B%281%2FP%5E%22%2A%22-1%29e%5E%28-r%29%29=5\"$ .
\n" ); document.write( "Let's solve for $\"r\"$ :
\n" ); document.write( " $\"+1%2F%281%2B%281%2FP%5E%22%2A%22-1%29e%5E%28-r%29%29=5\"$ --> $\"+1%2B%281%2FP%5E%22%2A%22-1%29e%5E%28-r%29=1%2F5\"$ --> $\"+%281%2FP%5E%22%2A%22-1%29e%5E%28-r%29=1%2F5-1\"$ --> $\"%281%2FP%5E%22%2A%22-1%29e%5E%28-r%29=-4%2F5\"$
\n" ); document.write( "Multiplying both sides times $\"-1\"$ we get
\n" ); document.write( " $\"%281-1%2FP%5E%22%2A%22%29e%5E%28-r%29=4%2F5\"$ --> $\"%28%28P%5E%22%2A%22-1%29%2FP%5E%22%2A%22%29e%5E%28-r%29=4%2F5\"$ --> $\"e%5E%28-r%29=%284%2F5%29%28P%5E%22%2A%22%2F%28P%5E%22%2A%22-1%29%29\"$ --> $\"e%5Er=%285%2F4%29%28%28P%5E%22%2A%22-1%29%2FP%5E%22%2A%22%29\"$ --> $\"e%5Er=5%28P%5E%22%2A%22-1%29%2F4P%5E%22%2A%22\"$ --> $\"r=ln%285%28P%5E%22%2A%22-1%29%2F4P%5E%22%2A%22%29\"$ \n" ); document.write( "

\n" );