Adouble-paned window has two glass panes separated by a layer of air. why
is air, rather than glass, used to fill this space?

The layer of air is used as an insulator. Otherwise the heat or cold would just travel through the glass.

The conduction of heat is slowed by the air

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.