Question

There were 55.5 million people enrolled in Medicare in 2015. In 2009, there were 46.6million enrolled. Which value best represents the unit rate of change (slope) in millions per year?a)-1.48b) 1.48c) 19.1%d) -0.674

Answer 1

Let the number of people enrolled in Medicare be represented by y

Let the year be represented by x

So that,

`\begin{gathered} (x_1,y_1)=(2015,55.5\text{ million)} \\ (x_2,y_2)=(2009,46.6\text{ million)} \end{gathered}`

The unit rate of change (slope) in millions per year can be calculated by:

`\begin{gathered} slope=(y_2-y_1)/(x_2-x_1) \\ \text{Hence,} \\ slope=\frac{46.6million_{}-55.5million_{}}{2009_{}-2015_{}} \\ slope=(-8.9)/(-6) \\ slope=1.48 \\ \end{gathered}`

Therefore, the unit rate of change in millions per year is 1.48 [Option B]