is the initial amount in the equation, so you should have plugged in 50 for
Also, you are right that we have to find out when it decays to 5, but the problem says A is the amount remaining after time t. They in fact mean A(t) is the amount remaining after time t, as the amount remaining is a function of how much you started with. So we need to solve and you will get approx 10.3.
For part c) the time it takes to decay to 10% of the original amount actually does not depend on the size of the initial amount. You can see this buy saying let X be the original amount. Then we have to see when it decays to .10*X.... so we solve
and you will get approx. 10.3