Answer: If the population of mosquitoes was quadrupling each year, then the population in any given year is four times the population of the previous year. Let M0 be the initial population of mosquitoes in 1998, then we can write:
Population of mosquitoes in 1999 = 4 * M0
Population of mosquitoes in 2000 = 4 * (4 * M0) = 16 * M0
Population of mosquitoes in 2001 = 4 * (16 * M0) = 64 * M0
Population of mosquitoes in 2002 = 4 * (64 * M0) = 256 * M0
In general, the population of mosquitoes in the year n (where n is the number of years since 1998) is given by:
Mn = 4^n * M0
Since the population of mosquitoes was 2750 in 1998, we can substitute n = 0 and M0 = 2750 in the above formula to get:
M0 = 2750
Therefore, the population of mosquitoes in the year n is:
Mn = 4^n * 2750
For example, the population of mosquitoes in the year 2002 (which is four years after 1998) is:
M2 = 4^2 * 2750 = 16 * 2750 = 44000
Note that this assumes that the conditions (e.g. weather, presence of predators, etc.) at the beach remain constant over time, which is not necessarily true in reality.
Explanation: