
Denote the state variable by $p$.
Using $n$ for the time point, we can denote the value of the state variable at a particular time point as $p_n$. Given the statement of the problem, define $p_n$ in words. Be sure to give units.
The state variable $p_n$ is the
of
in your blood measured in
(unit) that occurred $n$ intervals of 5
(unit) each after the injection of pencillin. In other words, $p_n$ is the concentration after
minutes.
Hint
Just fill in the blanks with the proper words or combination of symbols.
Online, you can enter mug for μg as μ is the Greek letter “mu,” or you can use the Greek symbol itself to enter it as μg.
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Specify the rule for going from one time step to the next.
$p_{n+1} =$
for $n=0,1,2, \ldots$
(Online, enter p_n for $p_n$.)
Hint
What happens to the concentration of penicillin in each time step? You need to know how much is left (not how much decayed away).
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Specify the initial conditions.
$p_0=$
Hint
You can read this right off the problem statement.
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Summarize by writing down the complete dynamical system, with evolution rule and initial condition.
$p_{n+1} = $
for $n=0,1,2, \ldots$
$p_0 = $
Evolve the dynamical system for four time steps
$p_0=$
$p_1=$
$p_2=$
$p_3=$
$p_4=$
Hint
Apply the rule four times, starting with the initial condition.
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What is the concentration of penicillin 10 minutes after the injection?
After 20 minutes?
Be sure to include units. Online, put units in second box.
Hint
10 minutes after the injection corresponds to how many time steps?
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