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(0) = ____

f(n) = f(n - 1) · 0.9 , for n ≥ 1

After 3 years, _____ birds will remain.

Answer 1

The recursively-defined function to describe this situation is:

• f(0) = 14000
• f(n) = f(n - 1) · 0.9 , for n ≥ 1
• After 3 years, 10206 birds will remain.

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
• f(3) = f(2) * 0.9 = 11340 * 0.9 = 10206

Therefore, the final number of birds after three years in decline is 10206.