Let's address the problem step by step.

Part a) What does $N(t)$ approach as $t \to \infty$?

The function given is:

$N(t) = \frac{0.7t + 800}{7t + 6}$

To find what $N(t)$ approaches as $t$ tends to infinity, we need to analyze the behavior of this function for very large values of $t$. As $t$ becomes very large, the terms with $t$ in them will dominate over the constants (800 and 6), so we can simplify the function by focusing on the leading terms:

$N(t) \approx \frac{0.7t}{7t} = \frac{0.7}{7} = 0.1$

Thus, as $t \to \infty$, $N(t) \to 0.1$.

The correct answer is C: 0.1.

Part b) Interpretation of the result:

The result $N(t) \to 0.1$ means that as time passes, the concentration of the medication in the body approaches 0.1 parts per million. This suggests that after a long time, the dosage stabilizes at a very low concentration, indicating that the medication is being absorbed or eliminated from the body, leaving only a small residual amount.

Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. How would the function behave for values of $t$ less than 15?
2. What is the initial concentration of the medication at $t = 15$?
3. How would the concentration change if the numerator and denominator coefficients were different?
4. What would happen if the medication had a higher concentration limit as $t \to \infty$?
5. Can this model be used to predict the half-life of the medication in the body?

Tip: When analyzing rational functions, always check the degree of the numerator and denominator to determine the function's end behavior.