Question: Simple Plot Issues

I was solving thos differential equiation using dsolve:

diff(P(t),t)=b*P(t)+m*t

dsolve({diff(P(t),t)=b*P(t)+m*t,P(t0)=P0});

where t0=2000 and P0=100 and m=9/50

Then, I found b setting at t=2001, P=2*P0=200, I applied fsolve to do this and the result was:

b=-1.5979...

To this point, Maple computes correctly. The problem starts when I tried to plot the result in a single 2D-graph (P vs t) using the computed value for b, the expression involved is:

P(t)=.1126460951*t-0.7049523744e-1-1.090463096*10^1390*exp(-1.597924898*t)

I wrote

plot( .1126460951*t-0.7049523744e-1-1.090463096*10^1390*exp(-1.597924898*t) , t=2000..2001);

The result was a blank plot, only the axes appeared even if I used the y=A..B option in the plot command. Is there a way to get the desired plot without having to evaluate the function at several points and then using this set of points to generate the plot: plot({[a,b],[c,d],[f,g]...})? (that worked, of course).

Thanks and regards.

P.S. I have used Maple for over 15 years now and I've plotted expressions even more complicated than this one, I found this very strange. I guess the 10^1390 has something to do this time, but I'm not sure...