Question

Nancy has 1 box of carrots. Each day, she picks another 1/2 box .How many boxes of carrots will Nancy have in 6 days? Write an equation, complete the table, and then graph to sove the problem. Let x = the number of days and let y = the number of boxes

Answer 1

Given :

Nancy has 1 box of carrots.

Each day, she picks another 1/2 box

So, the number of boxes will every day will increase by 1/2 box

this can be represented by following sequence:

1 , 1 1/2 , 2 , 2 1/2 , ......

The first term is : a = 1

And the common difference : d = 1/2

So, if the number of days = x

And the number of boxes = y

so,

`\begin{gathered} y=d\cdot x+a \\ \\ y=(1)/(2)x+1 \end{gathered}`

The graph and the table of the equation will be as shown in the following image :

How many boxes of carrots will Nancy have in 6 days ?

When x = 6

The number of boxes = 1/2 * 6 + 1 = 3 + 1 = 4 boxes