Based on the data given:
400 games were sold after 11 months
800 games were sold after 21 months
1500 games were sold after 36 months
We need to plot a graph of months against the number of games:
From the graph,
Yes, a single linear model is a reasonable option for the data
The equation of the graph is given by:
[tex]y\text{ = 0. 0226x + 2.344 }[/tex]Note that y represents the number of months and x represents the number of board games.
The number of board games sold after 48months simply means that y= 48. In order to get x, we substitute y = 48 into the model
[tex]\begin{gathered} 48\text{ = 0.0226x + 2.344} \\ 0.0226x\text{ = }48-2.344 \\ 0.0226x\text{ =45.656} \\ x=\frac{45.656}{0.0226}=2020.18\text{ (to 2 d.p)} \end{gathered}[/tex]Therefore, the estimated number of games sold after 48 months is 2020.
