Answer: 68,819 rabbits
Step-by-step explanation:
First find the annual rate of growth that took the number of rabbits from 9,400 in 1998 to 32,000 in 2006.
Use the future value formula:
Number of years = 2006 - 1998 = 8 years
Future value formula:
Future value = Current value * ( 1 + rate) ^ number of years
Assume 2006 is the future and 1998 is present.
32,000 = 9,400 * (1 + r) ⁸
32,000 / 9,400 = (1 + r)⁸
(1 + r)⁸ = 3.404255319
1 + r = ⁸√3.404255319
r = ⁸√3.404255319 - 1
r = 16.55%
Use that rate to find the number of rabbits in 2011:
= Current value * (1 + rate) ^ number of years
Number of years = 2011 - 2006 = 5 years
= 32,000 * ( 1 + 16.55%)⁵
= 68,819 rabbits
