The population of rabbits on an island is growing exponentially. In the year 1995, the population of rabbits was 1000, and by 1999 the population had grown to 1800. Predict the population of rabbits in the year 2003, to the nearest whole number.

Given:

The population of rabbits on an island is growing exponentially.

In the year 1995, the population of rabbits was 1000, and by 1999 the population had grown to 1800.

To find:

Expected population of rabbits in the year 2003, to the nearest whole number.

Solution:

The exponential growth model is:

Where, a is the initial value, b is the growth factor, t is the number of years.

Let y be the population of rabbits t years after 1995.

In the year 1995, the population of rabbits was 1000, it can be written as (0,1000) and by 1999 the population had grown to 1800, it can be written as (4,1800).

For (0,1000),

For (4,1800) and a=1000, we get

The required exponential model is:

        ...(i)

in year 2003, the number of years since 1995 is 8.

Putting t=8 in (i), we get

Therefore, the population of rabbits in the year 2003 is 3240.

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