Answer:
[tex] a_0 = 14000 [/tex]
[tex] a_{n} = 0.9a_{n - 1},~~ for ~n \ge 1 [/tex]
Step-by-step explanation:
Let "a" represent the population.
[tex] a_0 [/tex] is the initial population.
[tex] a_n [/tex] is the population at year n.
Since the population decreases 10% each year, that means that each year, the population is 90% of the previous year.
The initial population is 14,000.
Each year fater than, the population is 90% of the population of the previous year, or 0.9 time the population of the previous year.
[tex] a_0 = 14000 [/tex]
[tex] a_{n} = 0.9a_{n - 1}, ~~for ~n \ge 1 [/tex]
