Given that number of rabbits on January 1 = 150
We have to find some equation that can be used to find the number of rabbits after x years.
Given that the population of rabbits on a large island doubles every year.
So number of rabbits in 2nd year = 150*2
number of rabbits in 3rd year = 150*2*2=[tex] 150(2)^2 [/tex]
number of rabbits in 4th year = 150*2*2*2=[tex] 150(2)^3 [/tex]
In same way
number of rabbits in xth year = 150*2*2...=[tex] 150(2)^{(x-1)} [/tex]
In the xth year, population should be 4800
Hence the required equatino is
[tex] 4800=150(2)^{(x-1)} [/tex]
Question isn't asking for the value of x, so there is no need to solve this equation.
Hence final answer is [tex] 4800=150(2)^{(x-1)} [/tex].
