Need help finding the doubling time

Suppose you invest $1500 in an account that pays interest at a nominal rate of 4.5% per year compounded monthly.

a) How long will it take the investment to double?

b) What continuous annual interest rate would result in the same annual yield?

Please help with these these problems.

For a) I have set up the problem as 3000 = 1500(x)^t, solve for t, however I am stuck as to whether the x would be the effective rate or the nominal rate? Would I put in 1.045 (nominal rate) for x and solve for t or would I put in 1.045939825 (effective rate) in for x and solve for t?

For b) I don't even understand what they are asking for. Are we trying to find what is the rate and how would we set up this problem? On the left side would it be the formula 1500e^r*t = (something)? Please shed some light on this problem also.

Thank you so much