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

The number $\mathrm{N}$ (in millions) of cellular phone subscribers worldwide is shown in the table. (Midyear estimates are given.) $$\begin{array}{l}{\text { (a) Use the data to sketch a rough graph of } N \text { as a function of t. }} \\ {\text { (b) Use your graph to estimate the number of cell-phone sub. }} \\ {\text { scribers at midyear in } 1995 \text { and } 1999 .}\end{array}$$

The number $\mathrm{N}$ (in millions) of cellular phone subscribers
worldwide is shown in the table. (Midyear estimates are given.)
$$\begin{array}{l}{\text { (a) Use the data to sketch a rough graph of } N \text { as a function of t. }} \\ {\text { (b) Use your graph to estimate the number of cell-phone sub. }} \\ {\text { scribers at midyear in } 1995 \text { and } 1999 .}\end{array}$$

Key Concepts

Graphical Representation of Data

This concept involves plotting pairs of data points on a coordinate system where one axis represents the independent variable (time, t) and the other represents the dependent variable (the number of subscribers, N). Creating such a graph allows for a visual representation of how cellular phone subscriptions change over time and helps identify trends or patterns in the data.

Interpolation

Interpolation is the process of estimating the value of a function at a point within the interval of known data points. In the context of the problem, once the rough graph is drawn using the provided data, interpolation allows us to estimate the number of cellular phone subscribers for years (such as 1995 and 1999) for which direct data may not be provided.

Time Series Analysis

Time series analysis refers to methods and techniques used to analyze data collected or recorded at successive points in time. In this problem, by sketching a graph of subscribers over time, one is evaluating how subscriber numbers evolve, identifying trends, and making forecasts based on the observed pattern of growth.

Transcript

00:03 Hi, guys.

00:04 So today we'll be talking about number 19 from chapter one, section one, from calculus early transcendental.

00:12 So the problem says the number n in millions of cellular phone subscribers worldwide is shown in the table.

00:19 Mid -year estimates are given.

00:20 So here i've written out the years and the corresponding values for the number of cellular phone subscribers worldwide.

00:30 So part a is asking you to sketch a rough graph of n as a function of t.

00:35 So here i i've plotted all the values for the corresponding values of n for t.

00:44 For 1990, the value of n is 11.

00:50 So each line is 25 for n.

00:55 So 11 is just around the halfway point, as you can see here.

01:00 And then 1992 was 26.

01:03 That's a little bit above the first tick mark.

01:09 1994 was 60 and that's so that's between the second and the third tick mark 1996 was 160 which is above 100 and then you go two more tick marks and a halfway point so right there and then 1998 was 340 and then you go 300 you go 300 you go to 300 and then you go a little bit, like almost two tick marks above, but not quite.

01:51 And then 2 ,650, so that's all the way at the top.

01:54 And then we just assume that when t is zero or no years, then n would also be zero.

02:03 So in order to get the graph, you should connect the dots.

02:13 I will try it very roughly.

02:21 So as you can see here, there's somewhat of a j shape.

02:24 So the graph forms, and this means that the rate of increase is higher...

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