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
Since you provide two expressions, and they are not the same, how do we tell which to use?
The first is a(t+1)/24
The second is at/(t+12)
Just plug in
250 for a and
1 or 2/3 for t
to get the desired child doses.
To calculate the drug dose for young children using the given expressions, we can substitute the values of t and a and evaluate the expressions.
a. For a child of one year (t = 1):
Expression 1: (2t^3 + t^2 - t)a / (48t^2 - 24t)
Substituting t = 1 and a = 250mg:
(2(1)^3 + (1)^2 - (1)) * 250 / (48(1)^2 - 24(1))
=(2 + 1 - 1) * 250 / (48 - 24)
= 2 * 250 / 24
= 500 / 24
≈ 20.83 mg
Expression 2: (3t^2 - 2t)a / (3t^2 + 34t - 24)
Substituting t = 1 and a = 250mg:
(3(1)^2 - 2(1)) * 250 / (3(1)^2 + 34(1) - 24)
=(3 - 2) * 250 / (3 + 34 - 24)
= 1 * 250 / 13
= 250 / 13
≈ 19.23 mg
Therefore, the dose to the nearest unit for a child of one year using both formulas is approximately:
a. Expression 1: 21 mg
b. Expression 2: 19 mg
b. For an eight-month-old child (t = 0.67):
Expression 1: (2t^3 + t^2 - t)a / (48t^2 - 24t)
Substituting t = 0.67 and a = 250mg:
(2(0.67)^3 + (0.67)^2 - (0.67)) * 250 / (48(0.67)^2 - 24(0.67))
=(2(0.67^3) + 0.67^2 - 0.67) * 250 / (48(0.67^2) - 24(0.67))
= (2(0.302) + 0.448 - 0.67) * 250 / (48(0.448) - 24(0.67))
= (0.604 + 0.448 - 0.67) * 250 / (1.2856 - 0.8064)
= (0.382 - 0.67) * 250 / 0.4792
= (-0.288) * 250 / 0.4792
= -72 / 0.4792
≈ -150.15 mg
Expression 2: (3t^2 - 2t)a / (3t^2 + 34t - 24)
Substituting t = 0.67 and a = 250mg:
(3(0.67)^2 - 2(0.67)) * 250 / (3(0.67)^2 + 34(0.67) - 24)
=(3(0.67^2) - 2(0.67)) * 250 / (3(0.67^2) + 34(0.67) - 24)
= (3(0.448) - 2(0.67)) * 250 / (3(0.448) + 34(0.67) - 24)
= (1.344 - 1.34) * 250 / (1.344 + 22.78 - 24)
= 0.004 * 250 / 0.124
= 1 / 0.124
≈ 8.06 mg
Therefore, the dose to the nearest unit for an eight-month-old child using both formulas is approximately:
a. Expression 1: -150 mg
b. Expression 2: 8 mg
Note: It is important to consult a healthcare professional for accurate dosing instructions for infants and young children.