In "wikipedia" the infinite is defined as something without any bound or larger than any number.But in the computation, the program needs a value to do the calculations. One can not touch or reach infinity but for his own satisfaction he goes to a maximum extent. By using this, one can select a maximum value to solve the given problem. I am considering the 10^25 as the maximum extent for exp(at) where a> 0. With the maximum value we can find the "t" in the following way exp(at) = 10^25, t = 25*log(10)/a. By using this "t" value we can solve the plotting problem. I am writing a simple code about it and hoping that it will be the right answer.
function Exp(a)\n t = 25*log(10)/a\n t = ceil(t)\n time = 0:t/1000:t\n s = poly(0,'s')\n temptf = syslin('c',1/(s+a))\n y = csim('step',time,temptf)\n plot(y,time)\nendfunction