Question

Choose a simplified numerical expression that models the situation, and then solve theproblem by evaluating the expression.A farm currently has 10 large male cattle. The farmer adds a pregnant rabbit to increase thelivestock population. The novice farmer estimates that her rabbit population will double insize every month. Including the 10 cattle, how many animals will the farmer have after 7months?Simplified expression:See image below for answer options.

Answer 1

We are given that the population of rabbits will double every month, this means that the first month there will be 2 rabbits:

`M_1=2`

Now, the second month is double the first:

`M_2=2M_1=2(2)=2^2`

For the third month is double the second:

`M_3=2M_2=2(2)^2=2^3`

If we continue like this we will notice that the number of rabbits given the number of months "n" is:

`M_n=2^n`

For "n = 7" we have:

`M_7=2^7`

Now, the number of livestock is the number of rabbits plus the 10 male cattle, therefore, the expression is:

`10+2^7`

Solving the expression:

`10+2^7=10+128=138`

Therefore, the number of livestock after 7 months is 138.