Answer:
The rabbit population will reach 500 after 10 months.
Explanation:
According to the given data:
The initial number of rabbit's equals 2.
Number of rabbit's after 2 months =2x3= 6
Number of rabbit's after 4 months = 6x3=18
Number of rabbit's after 6 months = 18x3=54
Number of rabbit's after 8 months = 54x3=162
Thus we can see that the number of rabbit's form a Geometric series with common ratio =3 and initial term = 2
Now the general term of a geometric series with first term 'a' and common ratio 'r' is given by
[tex]T_{n+1}=ar^{n}[/tex]
Thus we need to find when the term becomes 500 thus using the given data we have
[tex]500=2\cdot 3^{n}\\\\3^{n}=250\\\\(n)log_3(3)=log_3(250)\\\\(n)=5.025\\\\[/tex]
Thus the fifth term (excluding the start term) will have a rabbit count of 500 now since each term has a time difference of 2 months thus sixth term will occur after [tex]5\times 2=10months[/tex]
