ITEM 18

Question

Some plastic chairs are designed to be stackable. After the first chair in the stack, each additional chair adds the same amount to the overall height of the stack. The table below shows the total height of the stack when there are 1, 2, 3, and 4 chairs in the stack. Which function models the height of a stack of n chairs?

Answer 1

Let h(n) represent the height of a stack of n chairs.

Based on the information given in the problem, we can see that the height of the stack increases by a constant amount with each additional chair. This means that the function that models the height of the stack of chairs is linear.

Using the data provided in the table:

n | h(n)
1 | 1 (height of 1 chair)
2 | 2 (height of 2 chairs)
3 | 3 (height of 3 chairs)
4 | 4 (height of 4 chairs)

The equation for a linear function is of the form y = mx + b, where m is the slope and b is the y-intercept.

In this case, the slope represents the constant amount that the height increases by with each additional chair. Since the height increases by 1 unit with each additional chair, the slope is 1.

Therefore, the function that models the height of a stack of n chairs is:

h(n) = n