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The population of rabbits on an island is growing exponentially. In the year 1998, the population of rabbits was 9400, and by 2006 the population had grown to 32000. Predict the population of rabbits in the year 2011, to the nearest whole number.

Sagot :

Parrain

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

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