SOLUTION: quantitative comparison t is an integer COl A: 1/1+2^t COL B: 1/1+3^t Is it correct to say you cannot determine which is larger without addition

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: quantitative comparison t is an integer COl A: 1/1+2^t COL B: 1/1+3^t Is it correct to say you cannot determine which is larger without addition      Log On


   

Question 982696: quantitative comparison
t is an integer
COl A: 1/1+2^t

COL B: 1/1+3^t

Is it correct to say you cannot determine which is larger without additional information.
My reasoning is if t is positive, the col a is larger. and if t is negative, the col b is larger.
Is this correct? Am I missing anything? Please explain. Thanks! :)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%5Et is larger than 2%5Et when t+%3E+0

So 1%2B3%5Et is larger than 1%2B2%5Et when t+%3E+0

Ultimately, 1%2F%281%2B3%5Et%29 is smaller than 1%2F%281%2B2%5Et%29 when t+%3E+0. The reciprocals make the relationship swap.
Eg: 6 > 5 so 1/6 < 1/5 (since 0.167 < 0.2)

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Note: if t+%3C+0, then everything flips. So if they say "t is an integer" then there isn't enough info. If they said "t is a POSITIVE integer" then that's enough info to figure out that col A is larger.