ODE simple problem

Hi, I have a two problems.
I'm trying to solve simple differential equation in the form of:
dA/dt=-k*t*A
initial conditions:
k=1
A=5e-4
At=5e-4
This equation is describing reaction kinetics. To be more precise, first order reaction.
My problem is that obtained kinetic curve, is rather sigmoidal not expotential as expected. I was trying to change time step without success.
My second problem is more complex.
dA/dt=-k*t*(A^0.75)
initial conditions:
k=1
A=5e-4
At=5e-4
ERROR:
Nonlinear solver did not converge.
Time : 0.3011554385215172
Attempt to evaluate non-integral power of negative number.
Last time step is not converged.
How to fix those problems? Any ideas?
Best regards
Marek