Question

Scientists released 8 rabbits into a new habitat in year 0. Each year, there were twice as many rabbits as the year before. How many rabbits were there after x years? Write a function to represent this scenario.

Answer 1

f(x)=8(2)^x

Explanation:

Answer 2

The function to represent the increasing number of rabbits per yer is
`f(x)=8*2^(x)`

Solution:

The number of rabbits released each year is 8.

During 0 year, there will be 8 rabbits;

During year 1, the number of rabbits will be
`8+8=16` (or)
`8* 2 = 16`

Similarly, during the year 2, the number of rabbits will be
`16+16=32` or
`16* 2 = 32`

So, according to the pattern we can conclude that the function would be

`f(x)=8*2^(x)`

where x is the number of years.

On year 4, the total number of rabbits will be
`f(4)=8*2^(4)` = 128