friends rule a method for calculating pediatric drug dosages

friend\'s rule a method for calculating pediatric drug dosages, is based on a child\'s age. If a denotes the adult dosage( in milligrams) and if t is the age of the child( in years), then the child\'s dosage is given by D(t)=0.08ta. if the adult dose of a substance is 500 mg, how much should a 4- year- old receive ?



please solve it with explane what you did

Solution

The equation for child\'s dosage related with a fraction of adult\'s dosage and child\'s age as

D(t) = 0.08 t a milligrams, where a is adult\'s dosage (in milligrams) and t is age of child in years.

Given that adult\'s dosage of certain substance, a = 500 milligrams, and t = 4 yaers

Substitute above values in Dosage formula to estimate the child\'s dosage as

D(4) = 0.08 x 500 x 4 = 8 x 5 x 4 = 40 x 4 = 160 milligrams

Thus, a child of age 4 years should be given 160 milligrams of that medicine.

Here, we just calculated the amount of medicine which is 0.08 fraction of an adult\'s dosage for 1 yaer old child to a 4 years, Child. For every successive years of age of child an amount of 0.08 a should be increased.

This is given in the formula for dosage D(t), of a child of t years age, and the computation is done on the basis of this formula.