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. f(1) = f(n) = f(n - 1) · , for n ≥ 2 After 3 years, birds will remain.

Answer 1

Answer: for plato family

f (1) = 14000

f(n) = f(n-1) . 0.9 , for n > 2

After 3 years , 11 ,340

Explanation:

14000

0.9

11,340

Answer 2

Realize that

f(1) = 14,000,

f(2) = f(1) * 0.9;

f(3) = f(2) * 0.9;

f(4) = f(3) * 0.9 ,...

So, the answer is:

f(1) = 14,000

f(n) = f(n-1) * 14,000 , for n ≥ 2

And after 3 years =>

f(3) = f(2)* 0.9 = f(1) * 0.9 * 0.9 = 14,000 * 0.9 * 0.9 = 11,340 birds will remain