Question

Instructions:Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). 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

The recursive function is;

f(n)=f(n-1)×0.9 for n≥2

After 3 years, 11340 birds will remain.

Explanation:

First the native population was 14,000 before decreasing started, hence this is your f(1)

f(1)=14000

⇒A decrease of 10% is similar to multiplying the native value of birds with 90%

New number of birds = native value × 90% ⇒f(1)×0.9

For second year , you multiply the value you get after the first decrease by 0.9 to get the new number of birds;

f(2)=f(1)×0.9= 0.9f(1)=0.9×14000=12600

For the 3rd year, the value of the second year,f(2) is then reduced by 10%. This is similar to multiplying value of f(1) by 90%

f(3)=f(2)×0.9=12600×0.9=11340

Apply the same for the 4th year and above, hence for nth year;

f(n)=f(n-1)×0.9 for n≥2