Question

select the correct answer from each drop - down menu.
a large manufacturing company models the number of workers it hired each year after 2010 using the function shown on the graph.
complete the statements describing the situation.
based on the model, the company hired approximately ▲ workers in 2019.
the ( r^{2} ) value for this model is 0.56, indicating that this function ▲ a good model of the data.

Explanation:

Step1: Identify the year 2019

Since the \(x -\)axis is "Years Since 2010", for the year 2019, \(t = 2019 - 2010=9\)

Step2: Locate \(t = 9\) on the graph

On the graph, when \(t = 9\), we look at the \(y -\)value (number of workers). By observing the graph (assuming a proper reading of the coordinate - like if we consider the scale of the \(y -\)axis and \(x -\)axis). If we assume the \(y -\)axis has a scale where each grid is \(50\) workers (for example, if we consider the general grid - based graph), and by visual inspection (a more accurate reading would require exact grid - to - value mapping which is approximated here). If we assume the point corresponding to \(t = 9\) is at \(y = 600\) (by following the trend of the curve and the grid - based placement of the data points).

Step3: Analyze the \(r^{2}\) value

The coefficient of determination \(r^{2}=0.56\). A value of \(r^{2}\) between \(0\) and \(1\) indicates a non - perfect fit. Since \(r^{2}=0.56\), it means that the model explains \(56\%\) of the variation in the data. A value of \(r^{2}=0.56\) is not extremely close to \(1\) (which would mean a very good fit) or \(0\) (which would mean a very poor fit). So, it is a moderately good model.

Answer:

Based on the model, the company hired approximately \(600\) workers in 2019. Since \(r^{2}=0.56\), this function is not a perfect fit (because \(r^{2}<1\)), but it is a moderately good model of the data (because \(r^{2}>0.5\) which is a common threshold for a "reasonable" fit in some basic analyses).