Answer: 6,656 rabbits.
Explanation:
The initial number of rabbits is 26.
We know that every 30 days, this number is doubled.
Then after 30 days, the population of rabbits is: 2*26
After other 30 days, the population will be: 2*(2*26) = 26*(2)^2
After another 30 days, the population will be: 2*26*(2)^2 = 26*(26)^3
The equation for this population can be written as:
P = A*(1 + 1)^(d/30)
where:
A is the initial population, in this case, 26
d is the number of days that have ben passed.
the denominator of 30 is because the population doubles every 3 days, so when d = 30, we will have that d/30 = 1, this is the first time that the population is doubled. When d = 60, d/30 = 2, this is the second time that the population is doubled, and so on.
Then our equation is:
P(d) = 26*(2)^(d/30)
The population after 240 days will be:
P(240) = 26*(2)^(240/30) = 6,656
So after 240 days, there will be 6,656 rabbits.