document.write( "Question 169770: Problem:\r
\n" ); document.write( "\n" ); document.write( "Suppose $8,000 is invested at interest rate k, compounded continuously, and grows to $11,466.64 in 6 years.
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\n" ); document.write( " a) Find the interest rate
\n" ); document.write( " b) Find the exponential growth function
\n" ); document.write( " c) Find the balance after 10 years
\n" ); document.write( " d) Find the doubling time.\r
\n" ); document.write( "\n" ); document.write( "Thank you.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #125253 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Problem:
\n" ); document.write( "Suppose $8,000 is invested at interest rate k, compounded continuously, and grows to $11,466.64 in 6 years.\r
\n" ); document.write( "\n" ); document.write( "a) Find the interest rate
\n" ); document.write( "
\r\n" );
document.write( "\"A=Pe%5E%28rt%29\" where \"A=11466.64\", \"P=8000\", \"t=6\"\r\n" );
document.write( "\r\n" );
document.write( "\"11466.64=%288000%29e%5E%28r%286%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"11466.64=8000e%5E%286r%29\"\r\n" );
document.write( "Divide both sides by \"8000\"\r\n" );
document.write( "\"1.43333=e%5E%286r%29\"\r\n" );
document.write( "\r\n" );
document.write( "Take natural logs of both sides:\r\n" );
document.write( "\r\n" );
document.write( "\"ln%281.43333%29=ln%28e%5E%286r%29%29\"\r\n" );
document.write( "Use fact that \"log%28B%2CB%5EA%29=A\"\r\n" );
document.write( "\r\n" );
document.write( "\"ln%281.43333%29=6r\"\r\n" );
document.write( "Divide both sides by 6:\r\n" );
document.write( "\"ln%281.43333%29%2F6=r\"\r\n" );
document.write( "Use calculator:\r\n" );
document.write( "\".0600000681=r\"\r\n" );
document.write( "\r\n" );
document.write( "We'll round that to \".06\" or \"matrix%281%2C2%2C6%2C%22%25%22%29\"\r\n" );
document.write( "\r\n" );
document.write( "---------------------\r\n" );
document.write( "

\n" ); document.write( "b) Find the exponential growth function
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\r\n" );
document.write( "\"A=Pe%5E%28rt%29\"\r\n" );
document.write( "\r\n" );
document.write( "Substitute \"8000\" for \"P\" and \".06\" for \"r\":\r\n" );
document.write( "\r\n" );
document.write( "\"A=8000e%5E%28.06t%29\"\r\n" );
document.write( "\r\n" );
document.write( "Your teacher may want you to write \"A\" in\r\n" );
document.write( "functional notation as \"A%28t%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"A%28t%29=8000e%5E%28.06t%29\".  Ask your teacher.\r\n" );
document.write( "\r\n" );
document.write( "-------------------\r\n" );
document.write( "

\n" ); document.write( "c) Find the balance after 10 years
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\r\n" );
document.write( "Substitute \"10\" for \"t\" in\r\n" );
document.write( "\r\n" );
document.write( "\"A=8000e%5E%28.06t%29\".  \r\n" );
document.write( "\"A=8000e%5E%28.06%2810%29%29\"\r\n" );
document.write( "\"A=8000e%5E%28.6%29\"\r\n" );
document.write( "\"A=14576.9504\"  \r\n" );
document.write( "\"matrix%281%2C4%2C++++A%2C+%22=%22%2C+%22%24%22%2C+14576.95+%29\"    \r\n" );
document.write( "\r\n" );
document.write( "--------\r\n" );
document.write( "

\n" ); document.write( "d) Find the doubling time.
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\r\n" );
document.write( "For $8000 to double, it must become $16000,\r\n" );
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document.write( "So we substitute $16000 for A and solve for t\r\n" );
document.write( "\r\n" );
document.write( "\"A=8000e%5E%28.06t%29\"  \r\n" );
document.write( "\r\n" );
document.write( "\"16000=8000e%5E%28.06t%29\"\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by 8000\r\n" );
document.write( "\r\n" );
document.write( "\"2=e%5E%28.06t%29\"\r\n" );
document.write( "\r\n" );
document.write( "Take natural logs of both sides:\r\n" );
document.write( "\r\n" );
document.write( "\"ln%282%29=ln%28e%5E%28.06t%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Use fact that \"log%28B%2CB%5EA%29=A\"\r\n" );
document.write( "\r\n" );
document.write( "\"ln%282%29=.06t\"\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by .06:\r\n" );
document.write( "\r\n" );
document.write( "\"ln%282%29%2F6=t\"\r\n" );
document.write( "\r\n" );
document.write( "\"11.55245301\"\r\n" );
document.write( "\r\n" );
document.write( "or a little over \"11%261%2F2\" years.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
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