Answer:
Explanation:
• The initial dose of the Insulin = 10 Units
The insulin breaks down by about 5% each minute, therefore:
• The decay rate, r= 5%
We want to determine the time it will take for the remaining dosage to be half (5 units) of the original dose.
We use the exponential decay function:
Substituting the given values, we have:
To solve for t, we change to logarithm form.
The ODE has an equilibrium point at
We want to be an unstable equilibrium solution - in other words, we want all solutions with initial condition
for
near 2 to diverge from
- so
.
Divergence from would require that for
, any solution is increasing, and for
, and solution is decreasing. In order for that to happen, we need
if , and
if .
Now we just pick to satisfy these conditions. An easy choice is
, which forces
, so that one possible ODE would be
I've attached a plot of the slope field to demonstrate the behavior of the solutions.
Step-by-step explanation:
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