Solve or NSolve doesn't give any solution in twelve hours

Questions
, ,
1

I typed

NSolve[((900/454) (1816000 E^(-200 t/681) (-1 + E^(1782 t/6583)))/
    2673) <= 50, t]

with an equality (50) or inequality (<=50), with Solve or NSolve, and wihin 12 hours I don’t get a solution.

What is wrong ?

bilik.miloslav@wanadoo.fr

2 
FindRoot[((900/454) (1816000 E^(-200 t/681) (-1 + E^(1782 t/6583)))/
     2673) == 50, {t, 1}]

{t -> 0.140216}

returns almost immediately. Since there are mulitple solutions, the one that you get will depend on the starting value you give to FindRoot.

3 
NSolve[((900/454) (1816000 E^(-200 t/681) (-1 + E^(1782 t/6583)))/2673) == 50, t, Reals]
(*{{t -> 0.1402163037}, {t -> 143.2657137}}*)

Took about 40 seconds on my PC.

For inequality, one is supposed to use Reduce[]. But it was taking long time on my end. You can also use FindInstance if you just want one solution:

FindInstance[((900/454) (1816000 E^(-200 t/681) (-1 + E^(1782 t/6583)))/2673) <= 50, t]
(* {{t -> 0}} *)
4

Many thanks, adding “Reals” solves the problem. I don’t know Reduce or FindInstance and I will look, thx again for your hints.