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------------------------------------------------ The recommended adult dosage for a drug is \( D \) (in mg). To determine the appropriate dosage \( c \) for a child of age \( a \), pharmacists use the equation:

\[ c = 0.0417D(a + 1) \]

Suppose the dosage for an adult is 500 mg.

(a) Find the slope. What does it represent?

- The maximum dosage for an adult
- The difference between an adult's dosage and a newborn's dosage
- The increase in dosage for each one-year increase in the child's age
- The maximum difference between an adult's dosage and a newborn's dosage
- The increase in dosage for each one-month increase in the child's age

(b) What is the dosage for a newborn?

mg

The slope of the equation c = 0.0417D(a + 1) can be found by differentiating the equation with respect to a. When differentiating, the variable D is treated as a constant. The derivative of c with respect to a is 0.0417D. Therefore, the slope is 0.0417D.

The slope represents the increase in dosage for each one-year increase in the child's age. For every one-year increase in the child's age, the dosage is increased by 0.0417D mg.

To find the dosage for a newborn, substitute a = 0 into the equation c = 0.0417D(a + 1). Plugging in a = 0 gives c = 0.0417D(0 + 1) = 0.0417D. Therefore, the dosage for a newborn is 0.0417D mg.

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