The number N (in millions) of US cellular phone subscribers...

The number $N$ (in millions) of US cellular phone subscribers is shown in the table. (Midyear estimates are given.) $$ \begin{array}{|c|c|c|c|c|c|c|} \hline t & 1996 & 1998 & 2000 & 2002 & 2004 & 2006 \\ \hline N & 44 & 69 & 109 & 141 & 182 & 233 \\ \hline \end{array} $$ (a) Use the data to sketch a rough graph of $N$ as a function of $t$. (b) Use your graph to estimate the number of cell-phone subscribers at midyear in 2001 and 2005.

The number $N$ (in millions) of US cellular phone subscribers is shown in the table. (Midyear estimates are given.)
$$
\begin{array}{|c|c|c|c|c|c|c|}
\hline t & 1996 & 1998 & 2000 & 2002 & 2004 & 2006 \\
\hline N & 44 & 69 & 109 & 141 & 182 & 233 \\
\hline
\end{array}
$$
(a) Use the data to sketch a rough graph of $N$ as a function of $t$.
(b) Use your graph to estimate the number of cell-phone subscribers at midyear in 2001 and 2005.

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Key Concepts

Scale and Axes

Scale and axes are fundamental to accurately plotting and interpreting data on a graph. Choosing appropriate scales for both the horizontal and vertical axes is critical to ensuring that the data is represented proportionally, which in turn aids in the correct estimation and analysis of trends.

Interpolation

Interpolation is the process of estimating a value within the range of two known data points on a graph. By drawing a smooth curve or line through the plotted points, one can approximate the value of the function at a point lying between established data points.

Function Representation

Function representation is the concept of expressing a relationship where one variable depends on another. In this context, the number of subscribers is seen as a function of time, illustrating how the subscriber count changes over the years.

Graphing Data

Graphing data involves plotting coordinate points on a graph where one axis represents the independent variable and the other represents the dependent variable. This technique is used to visually represent numerical relationships, making it easier to observe trends and patterns in the data.

Transcript

00:11 Okay, you want to create a sketch of the table given, and you could do that by hand if you wanted to sketch that.

00:22 You would have your small t on the horizontal, and you could just count by twos.

00:30 So you get two, four, six, and so on.

00:33 And then your capital t temperatures would be along the vertical.

00:37 What you can do is, like, show a little break in the graph and maybe start counting.

00:41 At like 66 and comp by twos there, 68 to 70 and so forth.

00:46 I did use my graph and calculator for this.

00:50 I can show you real quick in case you don't know how to do that.

00:54 What you can do is first you need to go to second, where's my calculator? there.

01:01 There it is.

01:02 Second y equals you need to turn stat plot on.

01:06 So i did that.

01:07 And then you need to go to the stat button.

01:10 And you can press enter on edit.

01:13 And you see i have the table in list one and list two.

01:17 And then you want to set your window so the x's fit your numbers in list one and your y's fit your numbers in list two.

01:25 I always go a little bit below and a little bit above the smallest and biggest numbers in each list.

01:30 So then i made that graph and now i'm going to carry that graph over to my whiteboard.

01:44 Okay, so there's our graph...

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