Question

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. After 1 year, the population of native birds is 14,000.Complete the recursively-defined function to describe this situation.1(1)=¡(n) = ((n - 1)After 4 years,. for 7 > 2birds will remain.

Answer 1

Given

the population of native birds in first year is 14,000

Decreasing rate = 10%

Find

f(1)

f(n)=f(n-1).--

population after 4 years

Explanation

given after 1 year , the population is 14,000

so , f(1) = 14,000

the population is decreasing 10 %

so , population decay =

$\begin{gathered} f(n)=f(n-1)(1-r)^n \\ f(n)=f(n-1)(1-0.1)^1 \\ f(n)=f(n-1)(0.9) \end{gathered}$

f(2) =

$\begin{gathered} f(1)(0.9) \\ 14000(0.9) \\ 12600 \end{gathered}$

f(3) =

$\begin{gathered} f(3)=f(2)0.9 \\ f(3)=12600(0.9) \\ f(3)=11340 \end{gathered}$

After 4 years ,

f(4) =

$\begin{gathered} f(4)=f(3)0.9 \\ f(4)=11340(0.9) \\ f(4)=10206 \end{gathered}$

Final Answer

Therefore ,

f(1) = 14000

f(n)=f(n-1),(0.9)

After 4 years , 10206 birds will remain