This statement
x(t) = t.*(exp(-0.15*t));
says to set the value of x at indexes given by t to the expression on the right-hand side. Indexes must be positive integers (1, 2, 3, ...), but t has some negative values and a zero value in it, so that's why the error happens.
In fact the syntax for what you want to do is slightly simpler. You can just say:
t = -20:1:20;
% no need to specify indexes into x, just set the whole thing:
x = t.*(exp(-0.15*t));
Then to plot:
plot(t,x)
