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# worksheet 2 - calc

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```									Heart rate module – worksheet 2                                    Calculus

The differential equation for cholesterol given in the Stella model is:

Scenario 1:

1.       Polly eats 3000 calories a day. She does not exercise and has a family history of high
cholesterol (value 2). Being a college student, she is totally unaware of the dangers of
high cholesterol, so she doesn’t see the need for medicine. Assuming no lifestyle
changes, and if her cholesterol is 183 mg/dl on her 20th birthday, find the following:
   Use Euler’s method with step size 0.25 years to determine her cholesterol on her 21st
birthday.
   How many iterations will it take to find her cholesterol at age 60?
   Explain why you are always traveling in the same direction along the solution “curve”
when doing these iterations.
   Go to http://www.ncsec.org and open the website. Go to Student Activities, and open the
Stella model. We will now check our answers to yesterday’s questions using this model.

2.       In ten years, Polly has accomplished many things. After getting married, she has had 3
children. She is a working mother, so she often eats fast food due to her busy schedule
(a 3000 calorie diet). She still does not have time to exercise. Find:
   What will happen to the solution curve at if she begins taking medication today? Why?
   Use Euler’s method using step size 0.25 years to find her cholesterol on her next
birthday.
   Why would we want a computer to do this?
   Go to the website again to check your answers for yesterday’s work.
Scenario 2:

1.        Ishmael eats 2200 calories a day and is also a college student. He plays intramural
basketball twice a week. He has a low to moderate family history of high cholesterol
(value 1). His cholesterol level on his 20th birthday was 216 mg/dl:
    Use Euler’s method with step size 0.25 years to find his cholesterol in 18 months.
    Assume Ishmael beings a 10% of the maximum dose of Lipitor™. How many iteration
will it take before his cholesterol reaches a normal level (below 200)? How old will he
be?
    When do you suggest Ishmael should stop taking his medication? Why or why not?

2.        Ishmael is now 40. He has two teenage sons, both in high school. He still plays
basketball twice a week. He now eats 2800 calories a day.
    What happens to the solution curve when his eating habits change?
    Calculate the new slope of this curve if he maintains this 2800 calorie diet and takes a
50%.
    How many iterations of Euler’s method with step size 0.25 years will it take to return to a
normal cholesterol level (below 200)?
    When he reaches this cholesterol level, what do you suggest for managing his cholesterol
level? Should he stay on medication? Increase or decrease his dose? Change his diet?
A combination of these? Which is best? Why?

*** Tomorrow in class we will use the Stella™ model to
check our work for Ishmael on both worksheets. If you
access to the internet at home, you may also use the model
to check your work. However, it is required that you
provide calculus reasoning and show your calculations for
this assignment! ***

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