document.write( "Question 225276: If all who hear a rumor repeat it to two people a day, and if 20 people start the rumor, then number of people N who have heard the rumor after t days is given by N(t) = 20(3)t. After what amount of time will 1000 have heard the rumor? \n" ); document.write( "
Algebra.Com's Answer #168167 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
\"N%28t%29+=+20%283%29%5Et\"
\n" ); document.write( "You're given n(t) =1000 and you've been asked to find t:
\n" ); document.write( "\"1000++=+20%283%29%5Et\"
\n" ); document.write( "So solve for t we're going to \"peel away\" the rest of the right side (i.e. the 20 and the 3). We'll start by dividing both sides by 20:
\n" ); document.write( "\"50+=+3%5Et\"
\n" ); document.write( "Next, to get rid of the 3, we will need to use logarithms. If 50 and \"3%5Et\" are equal then their logarithms are equal, too. (You should use a base for the logarithms that your calculator can handle. Usually base 10 or base e (aka natural) logarithms are best.):
\n" ); document.write( "\"log%28%2850%29%29+=+log%28%283%5Et%29%29\"
\n" ); document.write( "Now we can use the property of logarithms, \"log%28a%2C+%28b%5Ec%29%29+=+c%2Alog%28a%2C+%28b%29%29\", to \"move\" the t out of the exponent:
\n" ); document.write( "\"log%28%2850%29%29+=+t%2Alog%28%283%29%29\"
\n" ); document.write( "We can now solve for t by dividing both sides by \"log%28%283%29%29\":
\n" ); document.write( "\"log%28%2850%29%29%2Flog%28%283%29%29+=+t\"
\n" ); document.write( "For our final answer we can use our calculator on the two logarithms on the left side:
\n" ); document.write( "\"1.6989700043360188047862611052755%2F0.47712125471966243729502790325512+=+t\"
\n" ); document.write( "\"3.5608767950073117714936079297+=+t\"
\n" ); document.write( "Of course you can round off these decimals as you prefer. \n" ); document.write( "
\n" );