With T that large, you quickly end up with an array of Inf values.
This loop will do what you want:
A0 = 3;
k = 5;
I(1) = A0 * exp(100);
A(1) = I(1)*k;
for T = 2:100
I(T)= A(T-1).* exp(T+99);
A(T) = I(T)*k;
end
I started the loop counter at 1 rather than 100 because otherwise your arrays are padded with 99 zeros. That takes up memory.
