Generating An Exponential Function

I am trying to generate an exponential function which grows with factor 0.5

between -20 < t < 20.

Did I find it correct? I was not sure so that is why I just wanted to ask here.

Here is my code which I wrote:

t = -20 : 0.5 : 20;

unit=zeros(size(t));
unit(11:end) = 1;

expf = exp(0.5*t);
expunit = expf.*unit;

stem(t,expunit, '- b',... 
          'LineWidth',2);

[Dyuman Joshi]

factor of 5 how exactly?