The function $$ N(t)=\frac{0.8 t+1100}{3 t+4}, t \geq 15 $$, gives the body concentration $$ N(t) $$, in parts per million, of a certain dosage of medication after time $$ t $$, in hours. a) What does $$ N(t) $$ approach as $$ t $$ goes to $$ \infty $$ ? b) Explain the meaning of the answer to part a) in terms of the application.

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a) As $$ t $$ goes to $$ \infty $$, $$ N(t) $$ approaches $$ \frac{4}{15} $$ or approximately $$ 0.267 $$ parts per million. b) The steady-state concentration of the medication in the body is approximately $$ 0.267 $$ parts per million, indicating a balance between administration and elimination.

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