document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388750>Question 388750</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Elly invested money in an account with a fixed interest rate. The interest is compounded annually. After 5 years her balance was $2741.69, and after 10 years her balance was $3416.53.<BR>\n" );
document.write( "A.Find an exponential equation that models these data. (round the growth rate to thousandths.)<BR>\n" );
document.write( "B.How much did Elly orignally invest?<BR>\n" );
document.write( "C.What is the interest rate for the account? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #275160 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=275160\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Elly invested money in an account with a fixed interest rate. The interest is compounded annually. After 5 years her balance was $2741.69, and after 10 years her balance was $3416.53.<BR>\n" );
document.write( "A.Find an exponential equation that models these data. (round the growth rate to thousandths.<BR>\n" );
document.write( "A = amount invested, r = interest rate in decimal form<BR>\n" );
document.write( "@ 5 yrs: 2741.69 = A*(1 + r)^5<BR>\n" );
document.write( "@10 yrs: 3416.53 = A*(1 + r)^10<BR>\n" );
document.write( "2 variables, 2 equations<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "log(2714.69) = log(A) + 5*log(1+r)<BR>\n" );
document.write( "log(3416.53) = log(A) + 10*log(1+r)<BR>\n" );
document.write( "------------------------------------- Subtract 1 from 2<BR>\n" );
document.write( "0.0999865 = 5*log(1+r)<BR>\n" );
document.write( "log(1+r) = 0.019973<BR>\n" );
document.write( "1+r = 1.04706<BR>\n" );
document.write( "r =~ 4.7%<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "B.How much did Elly orignally invest?<BR>\n" );
document.write( "log(2714.69) = log(A) + 5*log(1+r)<BR>\n" );
document.write( "log(A) = log(2714.69) - 5*log(1.047) = 3.3339868<BR>\n" );
document.write( "A = $2157.68<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "C.What is the interest rate for the account? 4.7% </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );