a sheep breeding farm counted a total of 40 sheep on their grounds after one year the number of sheep doubled then in the next year the number of sheep doubled again if this trend continues which of the following options represents the number of sheep on the farm by then end of each year

Answer:
graph (b)

Explanation:
The farm started with 40 sheep and the number doubled each year.
So, the equation modeling this situation would be:
N(x) = 40*(2)^2
By getting the equation, we can notice that we already excluded the third and fourth choices as they have the wrong equations.

Now, we will need to select the right graph which is either graph a or graph b.
To do this, we will get the value of N(x) for different values of x as follows:
At x = 0: N(0) = 40*(2)^0 = 40
At x = 1: N(1) = 40*(2)^1 = 80
At x = 1: N(2) = 40*(2)^2 = 160

Now, taking a look at graph a, we will find that:
N(1) = 120
N(2) = 360
These numbers are not the same as the numbers we calculated, therefore, this graph is wrong

Taking a look at graph b, we will find that:
N(1) = 80
N(2) = 160
These numbers are exactly the same as the ones calculated, therefore, this graph is the correct one.

Hope this helps :)