Question

A series of tile patterns is shown below. Consider the function that represents the number of whitetiles in each figureFigure 1Figure 2Figure 3Figure 4Select all statements that are true.

Answer 1

Solution

From the figures, the right options are

1) w(n) = 4n + 4 represents the function

To prove this

n = 1,2,3,4 for the different figures respectively.

w(1) = 4(1) + 4 = 8 white tiles in the first figure

w(2) = 4(2) + 4 = 12 white tiles in the second figure

w(3) = 4(3) + 4 = 16 white tiles in the third figure

w(4) = 4(4) + 4 = 20 white tiles in the fourth figure

Hence the first option is right.

2) Input value for the functions are natural numbers as we can see from n = 1,2,3,4 ..... substituted to find the number of white tiles.

3) The function is continuous as n = 1, 2, 3, 4, 5, 6, 7, 8..........

4) Figure 8 will have 36 white tiles.

w(8) = 4(8) + 4 = 32 +4 = 36 white tiles