Cowlings rule is another function for determining the child’s dosage of a drug. For this rule, the formula of cowlings rule is:
d = D(a+1)/24
(expresses the child’s dosage d as a function of the adult dosage D and the child’s age a.)
a) If a doctor prescribes 1000 milligrams of acetaminophen for an adult, then how many milligrams would she prescribe for a six-year-old child using Cowling’s rule?
Solution
To find the dosage of acetaminophen for a six-year-old child using Cowling’s rule, we need to first convert the child’s age from years to months. Six years equal 72 months. We can then substitute the given values into the formula and solve for d:
d = 1000(72+1)/24 d = 1000(73)/24 d = 38,041.67/24 d ≈ 1583.40 milligrams
Therefore, a six-year-old child would require a dosage of approximately 1583.40 milligrams of acetaminophen using Cowling’s rule.
b) If a doctor uses Cowling’s rule to prescribe 200 milligrams of a drug to a child when she would prescribe 600 milligrams to an adult, then how old is the child?
Solution
To find the age of the child who requires 200 milligrams of a drug using Cowling’s rule, we can rearrange the formula to solve for a:
d = D(a+1)/24 d*24 = D(a+1) 24d/D = a+1 a = 24d/D – 1
We can then substitute the given values and solve for a:
200*24/600 – 1 = a 8 – 1 = a a = 7
Therefore, the child who requires 200 milligrams of the drug using Cowling’s rule is seven months old.
Explain what the variables in the formula represent and show all steps in the computations.
Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.):
- Literal equation
- Formula
- Solve
- Substitute
- Conditional equation
Solution
Cowling’s rule is a formula that can be used to calculate the child’s dosage of a drug based on the adult dosage and the child’s age. To use the formula, we need to substitute the given values and solve for the unknown variable. This formula is a literal equation, which can be rearranged to solve for different variables. The use of formulas and the ability to substitute and solve are essential skills in mathematics.
