Two expressions for calculating the drug dose for young children are:
(2t^3 + t^2 -t)a / 48t^2 -24t and (3t^2 -2t)a / 3t^2 + 34t - 24
where t is the age of the child in years and a is the adult dose. If the adult dose for a pain killing drug is 250mg, then what is the dose to the nearest unit for:
a. a child of one year
b. an eight month of child
thanks in advance everyone. this stuffs killing me
To calculate the drug dose for young children using the given expressions, you need to substitute the age of the child (t) into the expressions and multiply by the adult dose (a). In this case, the adult dose is 250mg.
a. To determine the dose for a one-year-old child, substitute t = 1 into both expressions:
Expression 1: (2(1)^3 + (1)^2 - 1)a / (48(1)^2 - 24(1))
Simplify the expression: (2 + 1 - 1)a / (48 - 24)
Calculate the expression: (2)a / (24)
Simplify further: 2a / 24
Expression 2: (3(1)^2 - 2(1))a / (3(1)^2 + 34(1) - 24)
Simplify the expression: (3 - 2)a / (3 + 34 - 24)
Calculate the expression: (1)a / (13)
Simplify further: a / 13
Now substitute a = 250mg into both expressions:
Expression 1: 2(250) / 24 = 500 / 24 = 20.83 mg (to the nearest unit: 21 mg)
Expression 2: 250 / 13 = 19.23 mg (to the nearest unit: 19 mg)
Therefore, the estimated dose for a one-year-old child is approximately 21 mg according to Expression 1 and 19 mg according to Expression 2.
b. To determine the dose for an eight-month-old child, substitute t = 0.67 (since eight months is roughly 2/3 of a year) into both expressions:
Expression 1: (2(0.67)^3 + (0.67)^2 - 0.67)a / (48(0.67)^2 - 24(0.67))
Calculate the expression: (0.92)a / 23.04
Substitute a = 250mg: (0.92)(250) / 23.04 = 10 mg
Expression 2: (3(0.67)^2 - 2(0.67))a / (3(0.67)^2 + 34(0.67) - 24)
Calculate the expression: (0.68)a / 13.54
Substitute a = 250mg: (0.68)(250) / 13.54 = 12.54 mg (to the nearest unit: 13 mg)
Therefore, the estimated dose for an eight-month-old child is approximately 10 mg according to Expression 1 and 13 mg according to Expression 2.