Lynch Kelley
12/25/2023 · Middle School
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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