Question

The table shows the total number of pictures Cal took by the end of each week. Cal's Pictures Week (w) Total Number of Pictures 1 4 2 2 8 3 12 4 16 Based on this pattern, which expression can be used to find the total number of pictures Cal took by the end of w weeks?

Answer 1

Let's begin by listing out the given information:

`(x,y)=(1,4),(2,8),(3,12),(4,16)`

From the data given, we will see that the data follows the expression shown below:

`\begin{gathered} Week1\colon(x)/(y)=(1)/(4) \\ Week2\colon(x)/(y)=(2)/(8)\Rightarrow(x)/(y)=(1)/(4) \\ Week3\colon(x)/(y)=(3)/(12)\Rightarrow(x)/(y)=(1)/(4) \\ Week4\colon(x)/(y)=(4)/(16)\Rightarrow(x)/(y)=(1)/(4) \\ \Rightarrow y=4x \\ \therefore y=4x \end{gathered}`

Therefore, the total number of pictures taken by Cal after w weeks is given by the expression: y = 4x