In how many years, approximately, from 1998 will the population of Nisos be as much as Queen Irene has proclaimed that the islands can support?
$\text{(A)}\ 50\text{ yrs.} \qquad \text{(B)}\ 75\text{ yrs.} \qquad \text{(C)}\ 100\text{ yrs.} \qquad \text{(D)}\ 125\text{ yrs.} \qquad \text{(E)}\ 150\text{ yrs.}$
We can divide the total area by how much will be occupied per person:
$\frac{24900 \text{ acres}}{1.5 \text{ acres per person}}=16600 \text{ people}$ can stay on the island at its maximum capacity.
We can divide 16600 by the current population in $1998$ which is 200 to see by what factor the population increases:
$\frac{16600}{200}=83$-fold increase in population.
Thus, the population increases by a factor $83$.  This is very close to $3 \times 3 \times 3 \times 3 = 81$, and so there are about $4$ triplings of the island's population.
It takes $4\times25=100=\boxed{C}$ years to triple the island's population four times in succession.