Answer
See below.
Work Step by Step
a) $N(t)=N_0e^{kt}$
b) We know that $2x=xe^{k\cdot18}\\2=e^{18k}\\18k=\ln2\\k=\frac{\ln2}{18}\approx0.038508176697774739412068451192120920448638896353347514117$
Thus $N(24)=10000e^{0.038508176697774739412068451192120920448638896353347514117\cdot24}\approx25198$