If the recommended adult dosage for a drug is \( D \) (in mg ), then to determine the appropriate dosage \( c \) for a child of age \( a \), pharmacists use the equation \( c=0.0417 D(a+1) \). Suppose the dosage for an adult is 400 mg . (a) Find the slope. What does it represent? the maximum difference between an adult's dosage and a newborn's dosage the difference between an adult's dosage and a newboin's dosage the increase in dosage for each one-year increase in the child's age the maximum dosage for an adult the increase in dosage for each one-month increase in the child's age (b) What is the dosage (in mg) for a newborn? mg

To find the slope of the equation \( c = 0.0417 D(a + 1) \), we can rewrite it in the slope-intercept format y = mx + b, where \( c \) represents the dosage for a child, \( D \) is the adult dosage, and \( a \) is the child’s age. Here, the slope \( m \) is represented by \( 0.0417D \), which indicates how much the dosage increases with each additional year of age in the child. Thus, the correct interpretation is the increase in dosage for each one-year increase in the child's age. (a) The slope is \( 0.0417 \times 400 = 16.68 \). For part (b), substituting \( a = 0 \) (representing a newborn) into the equation gives: \[ c = 0.0417 \times 400 \times (0 + 1) = 0.0417 \times 400 = 16.68 \, \text{mg}. \] So, the dosage for a newborn is approximately 16.68 mg. Now, here's some more fun context to illuminate the importance of drug dosing! When it comes to pediatric medicine, it's fascinating to note how the principles of pharmacology apply differently to kids: they often metabolize drugs differently than adults. This means that the stakes of getting the dose just right cannot be overstated! It’s not only about safety but also about ensuring efficacy in treatments for children. Also, it’s worth mentioning that age isn't the only factor affecting dosages! Weight can play an equally crucial role. That's why medical professionals often rely on weight-based dosing for accuracy. If you want to dive deeper into this critical topic, consider exploring the field of pediatric pharmacology to understand how these principles are applied in real-world scenarios!