SOLUTION: can you solve this without log? if yes, how do u solve this? a sequence t1, t2, t3, ... is defined by t1= 1000 and tn= 1.06tn-1, where n is a positive integer and n>

SOLUTION: can you solve this without log? if yes, how do u solve this? 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 th

Question 373821: can you solve this without log? if yes, how do u solve this?
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
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Consider
t(1) = 1,000 and t(n) = 1.06t(n-1). The 2nd equation gives . Then *...*. Hence
, or .
We want , or .
Take ln of both sides: , or . Thus n > 19.8542, so that .
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