We are given that the population of rabbits will double every month, this means that the first month there will be 2 rabbits:
[tex]M_1=2[/tex]
Now, the second month is double the first:
[tex]M_2=2M_1=2(2)=2^2[/tex]
For the third month is double the second:
[tex]M_3=2M_2=2(2)^2=2^3[/tex]
If we continue like this we will notice that the number of rabbits given the number of months "n" is:
[tex]M_n=2^n[/tex]
For "n = 7" we have:
[tex]M_7=2^7[/tex]
Now, the number of livestock is the number of rabbits plus the 10 male cattle, therefore, the expression is:
[tex]10+2^7[/tex]
Solving the expression:
[tex]10+2^7=10+128=138[/tex]
Therefore, the number of livestock after 7 months is 138.
