Determine the long-run behavior of the function: y= (7^t+4)/(4^t+6)

Question

y --> infinity as t --> infinity

y --> _____ as t--> -infinity

Answer 1

Divide the numerator and denominator by 4^t.

You should then immediately see that y => (7/4)^t which "blows up" (i.e. becomes unbounded) as t => ∞.