Question

PLEASE HELP!!!

A bird sanctuary initially contains 1000 birds. Each year, 10% of the birds fly away, so the sanctuary is restocked with 40 new birds. Write a recursive rule for the number an of birds at the start of the nth year.
I need An = ?

Answer 1

An = 0.9A(n-1) + 40

Explanation:

10% decrease means 100-10 = 90% of the previous

A1: 1000

A2: (90% of 1000) + 40 = 0.9(1000) + 40

A3: 0.9(0.9(1000) + 40) + 40

= 0.9²(1000) + 0.9(40) + 40

A4: 0.9(0.9²(1000) + 0.9(40) + 40) + 40

An = 0.9A(n-1) + 40

Answer 2

A(1) = 1000

A(2) = A(1) - A(1) x 10/100 + 40

A(3) = A(2) - A(2) x 10/100 + 40

=> A(n) = A(n-1) - A(n-1) x 10/100 + 40

Hope this helps!

:)