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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

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asked 2021-06-11
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{ } & \text{(millions)} & \text{Revenue per Subscriber Unit ($)}\ \text{2000} & \text{109.5} & \text{48.55}\ \text{2001} & \text{128.4} & \text{49.79}\ \text{2002} & \text{140.8} & \text{51.00}\ \text{2003} & \text{158.7} & \text{51.55}\ \text{2004} & \text{182.1} & \text{52.54}\ \text{2005} & \text{207.9} & \text{50.65}\ \text{2006} & \text{233.0} & \text{49.07}\ \text{2007} & \text{255.4} & \text{49.26}\ \text{2008} & \text{270.3} & \text{48.87}\ \text{2009} & \text{285.6} & \text{47.97}\ \text{2010} & \text{296.3} & \text{47.53}\ \text{2011} & \text{316.0} & \text{46.11}\ \text{2012} & \text{326.5} & \text{48.99}\ \text{2013} & \text{335.7} & \text{48.79}\ \text{2014} & \text{355.4} & \text{46.64}\ \text{2015} & \text{377.9} & \text{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)

2021-06-12

The scatter plot for the subscribers suggests a linear model because the points 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:
\(\displaystyle{m}=\frac{{{y}{2}-{y}{1}}}{{{t}{2}-{t}{1}}}=\frac{{{377.9}-{109.5}}}{{{15}-{0}}}\sim{17.9}\)
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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Table shows the number of wireless service subscribers in the United States and their average monthly bill in the years from 2000 through 2015.

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