Representations of linear functions
Medical prescriptions
Since the body of children is smaller than
that of adults, physicians prescribe lower dosages of medicine for children than
for adults. Medical researchers
have proposed several methods for determining the dosage
to be given to a child. This task presents several of these
methods, which you are asked to compare.
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Use the
Representation of functions
tool to present a value table and a graph for each correspondence rule (formula) shown below. What scale do you
choose for the graph, and why?
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What is the meaning of function values that are
smaller than 1? Larger than 1? Equal to 1?
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At what age is a person considered an adult according to
the various methods for determining dosage?
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Do the points of intersection of the graphs with the axes
have a meaning, and if so, what is it?
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At what age does a child receive half the adult dosage
according to each method?
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Which of the methods recommends the smallest and largest dosages, and how does the answer
depend on the child's age?
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Describe cases in which two of the methods prescribe the same dosage.
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Augsberger's Formula
Multiply the adult dosage by the number resulting from the following correspondence rule, in which x represents the child's age in years.
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For example, if the recommended adult dosage is 250 miligrams (miligram = 1/1000 of a gram) a day,
according to Augsberger's formula, the dosage for a 10 year-old child will be
150 miligrams. |
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Dilling's Formula
Multiply the adult dosage by the number resulting from the following correspondence rule, in which x represents the child's age in years.
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Young's formula
Multiply the adult dosage by the number resulting from the following correspondence rule, in which x represents the child's age in years.
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Bastedo's Formula
Multiply the adult dosage by the number resulting from the following correspondence rule, in which x represents the child's age in years.
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