I am trying to run a manipulate function for my calculus class and I believe I followed the professor’s instructions for writing it 100%. However, I am relatively new to Mathematica and I can’t seem to get the program to run. Any help? Program is pictured below.
Wrap Evaluate around the first argument of Plot: Plot[Evaluate[A[t] /. soln], ...
Restart Mathematica and, before you do anything else, scrape-n-paste this into the notebook
Manipulate[soln=NDSolve[{A'[t]==.08A[t]-12k,A[0]==20000},A,{t,0,5}];
Plot[A[t]/.soln,{t,0,10},PlotRange->{0,25000}],{{k,1},0,500}]
and tap and and see if your plot appears.
I don’t think that made any substantial changes to your code except for increasing the vertical plot range just a bit so you could see that the plot starts above the top edge of what you had specified.
If all that works then you can start adding back in your plot decorations one at a time and verifying that it works after each tiny change, so you can try to back out if it stops working at any point.
One possible reason for your difficulty is that Mathematica keeps a cache of previous calculations and a prior assignment might have been responsible for you not seeing what you needed. But there is probably no way of verifying that at this point.
NDSolve will evaluate to an InterpolatingFunction. In your code the domain of the NDSolve is {t, 0, 5}, however the Plot uses a domain of {t, 0, 10}. The interpolating function may not return accurate values outside of the domain over which it was generated.
Unless there is a reason for using a numeric solution, why not use the analytic solution?
soln = DSolve[{A'[t] == 8/100 A[t] - 12 k, A[0] == 20000}, A[t], t]
(* {{A[t] -> -50 (-400 E^(2 t/25) - 3 k + 3 E^(2 t/25) k)}} *)