Math Problem Statement

Goal Your task is to create tables for the corresponding child’s dosage for a given age of the child. Role You are a nurse in a community hospital. Audience Your audience is the community doctor. Situation You are a nurse in a community hospital. You are particularly assigned to cater to children. To be able to efficiently perform your duties, you wish to come up with a table for the dosage of medicine for children, following Young’s rule. Young’s rule is used in medicine to convert adult dosage of medicine for children. Given that � is the child’s age, � is the adult dosage of a medicine, and � is the corresponding child’s dosage of the medicine, Young’s rule states that � = � � + 12 � = �� � + 12 Product, Performance, and Purpose You will prepare the following output for this task: a written copy of the table and the computations, and the graph of the function. • You are to create tables for the corresponding child’s dosage for a given age of the child. You are to do this for � = 10 mg, 25 mg, 50 mg, and 100 mg. Performance Task General Mathematics • Grade 11 2 • As a requirement for this unit, you are to present the graph of the function �(�) for the four different dosages. This means you have to show four graphs. You have to show your complete solution in finding the intercepts and asymptotes whenever they apply. You may use the table below as a guide. 10 mg 25 mg 50 mg 100 mg Age Dosage Age Dosage Age Dosage Age Dosage 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 11 11 11 11 12 12 12 12 You may use a spreadsheet file to easily fill up the table. Performance Task General Mathematics • Grade 11 3 Standards and Criteria Table 5.1. Learning outcome or task description for the output-based rubric Criteria Below Expectation (0–49%) Needs Improvement (50–74%) Successful Performance (75–99%) Exemplary Performance (99+%) Accuracy (40%) The dosage in the table should be accurate based on Young’s rule, and the graph should be accurate as well. Below 80% of the entries in the table and graphs are accurate. 81% to 89% of the entries in the table and graphs are accurate. 90% to 99% of the entries in the table and graphs are accurate. 100% of the entries in the table and graphs are accurate. Application of Concepts Learned (30%) The application of graphing rational functions must be evident in the performance task. Only two of the concepts learned in the unit are applied in the task. Only two of the concepts learned in the unit are applied in the task. Only three of the concepts learned in the unit are applied in the task. All pertinent concepts learned in the unit are applied in the task. Completeness and Detail (30%) The computations The computations and solutions lack a large amount of The computations and solutions lack a small amount of The computations and solutions needed to understand the The computations and solutions needed to understand the Performance Task General Mathematics • Grade 11 4 and solutions are complete, understandable , and thoroughly explained. detail enough to be understood. detail enough to be understood. report are complete. report are complete and thoroughly explained.

Solution

Analysis of the Graphs

The graphs show the child’s dosage as a function of age for different adult dosages (10 mg, 25 mg, 50 mg, and 100 mg) based on Young’s rule. Each curve represents how the dosage increases with the child's age:

  • As the child’s age increases, the dosage gradually approaches half of the adult dosage.
  • The shape of each graph reflects the rational function C(age)=A×ageage+12C(\text{age}) = \frac{A \times \text{age}}{\text{age} + 12}.
  • There are no asymptotes within the given range, and the graph is continuously increasing.

Key Points:

  1. Intercepts: All graphs start near zero, showing that very young children receive minimal doses.
  2. Behavior: The dosage approaches half the adult dosage but never exceeds it for the given range.
  3. Age Influence: The older the child, the closer the dosage gets to the halfway point of the adult dosage.

Would you like more detailed calculations or have any specific questions?

Related Questions:

  1. How does Young's rule compare to other pediatric dosing rules?
  2. What would the dosage be if the adult dosage were higher, such as 200 mg?
  3. Can Young's rule be used for infants (under 1 year)?
  4. What are the clinical implications of inaccurate dosage calculations?
  5. How does Young's rule account for other factors like weight?

Tip: Always verify the suitability of dosage formulas like Young’s rule for specific medications, as not all drugs have linear relationships with age.

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Math Problem Analysis

Mathematical Concepts

Rational Functions
Graphing
Interpolation

Formulas

C = (A × age) / (age + 12)

Theorems

Young's Rule for Pediatric Dosage

Suitable Grade Level

Grades 11-12