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# Table shows the number of wireless service subscribers in the United States and their average monthly bill in the years from 2000 through 2015. \begin

Transformations of functions
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asked 2021-05-23

Table shows the number of wireless service subscribers in the United States and their average monthly bill in the years from 2000 through 2015.

$$\begin{matrix} \text{Year} & \text{Subscribers} & \text{Average Monthly}\\ { } & \text{(millions)} & \text{Revenue per Subscriber Unit ()}\\ {2000} & {109.5} & {48.55}\\ {2001} & {128.4} & {49.79}\\ {2002} & {140.8} & {51.00}\\ {2003} & {158.7} & {51.55}\\ {2004} & {182.1} & {52.54}\\ {2005} & {207.9} & {50.65}\\ {2006} & {233.0} & {49.07}\\ {2007} & {255.4} & {49.26}\\ {2008} & {270.3} & {48.87}\\ {2009} & {285.6} & {47.97}\\ {2010} & {296.3} & {47.53}\\ {2011} & {316.0} & {46.11}\\ {2012} & {326.5} & {48.99}\\ {2013} & {335.7} & {48.79}\\ {2014} & {355.4} & {46.64}\\ {2015} & {377.9} & {44.65}\\ \end{matrix}$$

One of the scatter plots suggests a linear model. Use the points at t = 0 and t = 15 to find a model in the form y = mx + b.

## Answers (1)

2021-05-24

The scatter plot for the subscribers suggests a linear model because the point appear to lie on a line.
Use $$(t_1,y_1)=(0.109.5)$$ and $$(t_2,y_2)=(15,377.9)$$ to find the slope:
$$m=(y_2-y_1)/(t_2-t_1)=(377.9-109.5)/15 ~ 17.9$$
Since the y-intercept is the y-value when t=0, we know that b=109.5 from the first point. So, the equation is:
$$y=17,9t+109.5$$

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