document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=619340>Question 619340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The intensity of light is reduced by 2% for each metre that a diver descends below the surface of the water. At what depth is the intensity of light only 10% of that at the surface? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #389579 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=389579\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the intensity of light is reduced 2% for each meter that a diver descends below the surface.<BR>\n" );
document.write( "if the intensity starts at 100, then after 1 meter, the intensity is 100 - .02*100 which is equivalent to 100 * (1-.02) which is equivalent to .98 * 100<BR>\n" );
document.write( "the next meter reduces it another 2%.<BR>\n" );
document.write( "you get (.98*100) - .02*(.98*100) which is equivalent to (.98*100) * (1-.02) which is equivalent to (.98*100) * .98 which is equivalent to 100 * (.98)^2<BR>\n" );
document.write( "each additional meter reduces it by another addition to the exponent.<BR>\n" );
document.write( "for 10 meters, the reduction is 100 * (.98)^10<BR>\n" );
document.write( "the formula is, therefore:<BR>\n" );
document.write( "reduction in visibility = 100% * .98^m<BR>\n" );
document.write( "where m is equal to the number of meters.<BR>\n" );
document.write( "you want to know how many meters to reduce the visibility to 10%.<BR>\n" );
document.write( "the equation becomes:<BR>\n" );
document.write( "10% = 100% * .98^m<BR>\n" );
document.write( "you want to solve for m.<BR>\n" );
document.write( "divide both sides of this equation by 100% to get:<BR>\n" );
document.write( "10% / 100% = .98^m<BR>\n" );
document.write( "this results in:<BR>\n" );
document.write( ".1 = .98^m<BR>\n" );
document.write( "take the log of both sides of this equation to get:<BR>\n" );
document.write( "log(.1) = log(.98^m)<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "log(.1) = m*log(.98)<BR>\n" );
document.write( "divide both sides of this equation by log(.98) to get:<BR>\n" );
document.write( "m = log(.1) / log(.98)<BR>\n" );
document.write( "use your calculator to solve for m to get:<BR>\n" );
document.write( "m = 113.9740856<BR>\n" );
document.write( "the visibility should be reduced to 10% at 113.9740856 meters.<BR>\n" );
document.write( "100% * (.98)^(113.9740856) is equal to 10%<BR>\n" );
document.write( "to determine if your formula is correct, use a much smaller number.<BR>\n" );
document.write( "assume you want to know how much visibility you have after 3 meters.<BR>\n" );
document.write( "your equation becomes:<BR>\n" );
document.write( "100% * (.98)^3 which becomes 94.1192<BR>\n" );
document.write( "you should only have 94.1192% visibility after 3 meters if the equation is correct.<BR>\n" );
document.write( "start with 100% and reduce it by 2% to get 98<BR>\n" );
document.write( "reduce 98 by 2% to get 96.04<BR>\n" );
document.write( "reduce 96.04 by 2% to get 94.1192<BR>\n" );
document.write( "looks like the formula is good.<BR>\n" );
document.write( "your answer is 113.9740856 meters of depth reduces visibility to 10%.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "principle of logarithms used.<BR>\n" );
document.write( "log(a^b) = b*log(a)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );