Question

The native bird population in a city is decreasing at a rate of 10% per year due to industrialization of the area by humans. The population of native birds was 14,000 before the decrease began.
Complete the recursively-defined function to describe this situation.

Answer 1

Answer:

$a_0 = 14000$

$a_{n} = 0.9a_{n - 1},~~ for ~n \ge 1$

Step-by-step explanation:

Let "a" represent the population.

$a_0$ is the initial population.

$a_n$ 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.

$a_0 = 14000$

$a_{n} = 0.9a_{n - 1}, ~~for ~n \ge 1$