document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70181>Question 70181</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. If $4000 is deposited into an account paying 3% interest compounded annually and at the same time $2000 is deposited into an account paying 5% interest compounded annually, after how long will the two accounts have the same balance?  Round to the nearest year and show all work.<BR>\n" );
document.write( "2.  Would you prefer that your salary be modeled exponentially or logarithmically?  Explain your answer<BR>\n" );
document.write( "3.  If the half-life of a radioactive substance is 45 minutes and you originally have 2500 grams of the substance, how much will be left after 3 hours?  Explain how to determine the amount without using the exponential model.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #50061 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=50061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. If $4000 is deposited into an account paying 3% interest compounded annually and at the same time $2000 is deposited into an account paying 5% interest compounded annually, after how long will the two accounts have the same balance? Round to the nearest year and show all work.<BR>\n" );
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document.write( "4000(1+0.03)^t = 2000(1+0.05)^t<BR>\n" );
document.write( "2000=[(1.05)^t]/[1.03]^t<BR>\n" );
document.write( "2000= [1.019417478]^t<BR>\n" );
document.write( "Take the log of both sides to get:<BR>\n" );
document.write( "t=(log2000/log1.019417478]<BR>\n" );
document.write( "t=395.23 yrs.<BR>\n" );
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document.write( "2. Would you prefer that your salary be modeled exponentially or logarithmically? Explain your answer<BR>\n" );
document.write( "Y=ab^x is an increasing function so long as a and b are positive<BR>\n" );
document.write( "and x represents successive years.<BR>\n" );
document.write( "y=log x is also an increasing function but increases much more <BR>\n" );
document.write( "slowly than the exponential fuction.<BR>\n" );
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document.write( "3. If the half-life of a radioactive substance is 45 minutes and you originally have 2500 grams of the substance, how much will be left after 3 hours? Explain how to determine the amount without using the exponential model.<BR>\n" );
document.write( "A(t)=2500(1/2)^(t/45) where t is minutes elapsed<BR>\n" );
document.write( "3 hrs is 180 minutes<BR>\n" );
document.write( "A(180)= 2500(1/2)^(180/45)<BR>\n" );
document.write( "=2500(1/2)^4<BR>\n" );
document.write( "=2500/16<BR>\n" );
document.write( "=156.25 grams<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " \r<BR>\n" );
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