The recursively-defined function to describe this situation is:
f(0) = <u>14000</u>
f(n) = f(n - 1) · 0.9 , for n ≥ 1
After 3 years, <u>10206</u> birds will remain.
Step-by-step explanation:
To solve the number of birds that there will be after three years, you must recognize that the function f(0) means the number of birds at time zero, in which the birds are complete (that is, the 14,000 birds), by their part, following the equation provided below we have the following calculation:
f(n) = f(n-1) * 0.9
So:
f(1) = f(0) * 0.9 = 14000 * 0.9 = 12600
f(2) = f(1) * 0.9 = 12600 * 0.9 = 11340
<u>f(3) = f(2) * 0.9 = 11340 * 0.9 = 10206
</u>
Therefore, <u>the final number of birds after three years in decline is 10206</u>.