Gregory planted a lemon tree in his back yard. When he planted the tree, it was $2$ feet tall. He noticed that it has been growing $3$ inches every week.  

1. Create multiple representations ( $x → y$ table, graph, and equation) to represent the relationship between the days that have passed and the height of the tree.

   Hint (a):

   Remember, there are $12$ inches in a foot. Start with a table.

   How tall is the tree on day 0, the day it was planted?

   Use what you know about how it grows to generate the rest of the table.

   Answer (a):

   $\left. \begin{array} { c | c } { x } & { y } \\ \hline 0 & { 24 } \\ { 1 } & { 27 } \\ { 2 } & { 30 } \\ { 3 } & { 33 } \\ { 4 } & { 36 } \\ { 5 } & { 39 } \end{array} \right.$

   

   $y = 3x + 24$

2. If the tree continues growing at this rate, when will it be $6$ feet tall? How can you see this in each of the representations?

   Hint (b):

   How many inches are there in $6$ feet?

   More Help (b):

   Where do you see that on the table? On the graph? Describe it.

   Substitute $72$ for $y$ in the equation and solve for $x$.

   Answer (b):

   $16$ weeks.

3. State the possible inputs and outputs of the graph.

   Answer (c):

   Possible inputs: all number greater than and including $0$. Possible outputs: all numbers greater than and including $24$.