# portfolio problem:  the diastolic number in blood

PORTFOLIO PROBLEM:  The Diastolic Number in Blood Pressure

This project is adapted from an exercise problem of the college math text: Algebra and Trigonometry by Stewart, 3rd Edition.

DIRECTIONS FOR COMPLETING THE PORTFOLIO PROJECT

In this project you will investigate the relationship between the time of day and its affect on the diastolic reading of blood pressure.  (The diastolic reading is the bottom number of a blood pressure count.)

Everyone’s blood pressure varies over the course of the day.  In a certain individual, the resting diastolic blood pressure at time t is

B(t) =where t is measured in hours since midnight and B(t) in mmHg (millimeters of mercury).  Find the person’s diastolic blood pressure at 12:00 am using the value 0 for t.  You will now find the value of B(t) for each hour on the hour until 12:00 am the next day and analyze the results.

Part 1

1. Design a table or tables to show the following information:

1.         the number of hours past midnight using input values from 0 to 24 going in intervals of 1 hour

2.         the diastolic number rounded to the nearest hundredth

2. Describe a numerical pattern that you observe based on the table.  Please note maximum, minimum and middle values.

3.  If were a nurse talking to this patient on the phone and the patient is concerned that his diastolic number was 87, (7 points higher than the safe number of 80) explain what you would advise to the patient.

Criteria:

3.     Each table is labeled appropriately.

4.     The data is neatly organized in a way that anyone can understand.

5.   Your explanations of questions 2 and 3 are written clearly and can easily be understood by anyone reading your work.

Part 2

1. Use the data from your table(s) in Part 1 to graph the relationship between time and the diastolic value of the blood pressure count.

2. Label on the graph the maximum/minimum values, the period length, midline and the amplitude.

Criteria

6. ·         The axes are clearly labeled with Time and Diastolic Blood Pressure in mmHg. Decide which is the independent variable and which is the dependent variable.

7. ·         The scale is clearly indicated on each axis.

1.

### Criteria

1.  All variables are clearly identified.

2. Your explanations are written so that anyone can understand your meaning.

3.  The equations express the relationships or functions correctly:

4. variables are in the correct places;

5. correct operations (add, subtract, multiply, divide) are indicated.

Reflective Essay

Write a reflective essay to summarize your work. Include in your essay an explanation of the problem you were working to solve. Explain what you learned by doing this project.  For instance, explain the relationship between the period length, midline and the amplitude found on the graph and what it means in terms of the blood pressure count.

Your essay should cover at least one side of a sheet of loose-leaf paper. You should use good writing skills.

FINISHED PROJECT

7. ·         Your finished project should be arranged in order, with each part clearly marked.

8. ·         Each part meets its criteria.

9. ·         All required information is clearly stated in such a way that anyone can follow your reasoning.

10. ·         Your work is neatly done and shows evidence of use of proper tools and calculation techniques.

11. ·         You have given credit to any resources you used, including any people you may have consulted.

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