Question

1. many pediatric doses of drugs should be based on the childs surface area. the mosteller formula is often used for this purpose. to determine the surface area (in square meters), the childs height (in inches) and weight (in pounds) are multiplied together; this number is divided by 3131 and then a square root is taken of the result.

a. the mosteller formula is described in the problem above. write this as a formula using variables and mathematical symbols.
b. use this formula to find the surface area of a child who is 4 feet tall and weighs 75 pounds. note: you will need to first convert the height into just inches.
b. to get the dosage of an allergy medicine for a child, the following formula is used: $d = \frac{25\times a}{1.73}mg$. where a is the body surface area. calculate the dosage of this allergy medicine for this child.

Explanation:

Step1: Define variables and write Mosteller formula

Let $h$ be the height in inches and $w$ be the weight in pounds. The Mosteller formula for surface - area $A$ (in square meters) is $A=\sqrt{\frac{h\times w}{3131}}$.

Step2: Convert height to inches

Since 1 foot = 12 inches, a 4 - foot - tall child has a height $h = 4\times12=48$ inches. The weight $w = 75$ pounds. Substitute $h = 48$ and $w = 75$ into the Mosteller formula: $A=\sqrt{\frac{48\times75}{3131}}=\sqrt{\frac{3600}{3131}}\approx\sqrt{1.15}$. So, $A\approx1.07$ square meters.

Step3: Calculate allergy - medicine dosage

The formula for the dosage $D$ of allergy medicine is $D=\frac{25\times A}{1.73}$ mg. Substitute $A = 1.07$ into the formula: $D=\frac{25\times1.07}{1.73}=\frac{26.75}{1.73}\approx15.46$ mg.

Answer:

a. $A=\sqrt{\frac{h\times w}{3131}}$
b. The surface area is approximately $1.07$ square meters.
c. The dosage of the allergy medicine is approximately $15.46$ mg.