document.write( "Question 373821: can you solve this without log? if yes, how do u solve this?\r
\n" ); document.write( "\n" ); document.write( "a sequence t1, t2, t3, ... is defined by t1= 1000 and tn= 1.06tn-1, where n is a positive integer and n>_ 2. find the smallest value of n such that tn>3000 \n" ); document.write( "

Algebra.Com's Answer #266028 by robertb(5830) $\"\"$ $\"About$

You can put this solution on YOUR website!
Consider
\n" ); document.write( "t(1) = 1,000 and t(n) = 1.06t(n-1). The 2nd equation gives $\"t%28n%29%2Ft%28n-1%29+=+1.06\"$ . Then $\"%28t%28n%29%2Ft%28n-1%29%29%2A%28t%28n-1%29%2Ft%28n-2%29%29\"$ *...*

. Hence
\n" ); document.write( " $\"t%28n%29%2F1000+=+1.06%5E%28n-1%29\"$ , or $\"t%28n%29+=+1000%2A1.06%5E%28n-1%29\"$ .
\n" ); document.write( "We want $\"1000%2A%281.06%29%5E%28n-1%29%3E3000\"$ , or $\"%281.06%29%5E%28n-1%29%3E3\"$ .
\n" ); document.write( "Take ln of both sides: $\"%28n-1%29ln1.06%3Eln3\"$ , or $\"n-1+%3E+ln3%2Fln1.06+=+18.8542\"$ . Thus n > 19.8542, so that $\"n%3E=20\"$ . \n" ); document.write( "

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