Novocaine Example

> restart;

Initial Condition: .
Recursion Formula: .
Define the function directly from the difference equation.
This is called a recursive definition.

> u := proc(n) if n<=0 then 500 else u(n-1) - 0.2*u(n-1) fi end;

We can now evaluate for various values on simply by entering .

> u(0); u(1); u(2); u(3);

We can generate a list of points for taking on the values from 0 to 25 by entering .

> [seq([n,u(n)], n=0..25)];

We can avoid printing out the entire list, but save it for future use by assigning the list to a variable and by terminating the command with a colon.

> pts := [seq([n,u(n)], n=0..25)]:

We can plot the list of points using the plot command.

> plot(pts,style=point);

Upon reflection, we see that we can write in a closed form as .
What happens if we simply replace by and let take on arbitrary values?

> u := proc(t) 500*(0.8)^t end;
plot(u(t),t=0..25);

We can display both plots by giving each one a name, supressing any output,
and displaying them with the plots[display] command.

> P1 := plot(pts,style=point):
P2 := plot(u(t),t=0..25):
plots[display]({P1,P2});