The population t later is:

p(t) = p(0) e^{lambda t}

so:

340 = 182 e^{lambda 18}

18 lambda = ln(340/182) ~= 0.624939

lambda = 0.03471883.

For the doubling time t_2, we have:

364 = 182 e^{0.03471883 t_2}

so:

t_2 = ln(2)/0.03471883 ~=19.9646

So to the nearest 1/10th of a day the doubling time is 20 days.

RonL