Question

Help me please! It’s an emergency!! A small company is selling a new board game, and theyneed to know how many to produce in the future.They sold a total of 400 games after 11 months, 800games after 21 months, and 1500 games after 36months. Is a single linear model a reasonable option for this data? Use this to estimate the number of games sold after 48 months. Explain.

Answer 1

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:

`y\text{ = 0. 0226x + 2.344 }`

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

`\begin{gathered} 48\text{ = 0.0226x + 2.344} \\ 0.0226x\text{ = }48-2.344 \\ 0.0226x\text{ =45.656} \\ x=(45.656)/(0.0226)=2020.18\text{ (to 2 d.p)} \end{gathered}`

Therefore, the estimated number of games sold after 48 months is 2020.