Question

The table below shows the year and the number of people unemployed in a particular city for several years. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the number of unemployed reach 5?YearNumber Unemployed1990750199267019946501996605199855020005102002460200442020063802008320Using this tool we find the linear regression line to be y=Answer Type your answer without spaces or commas and rounded to the nearest hundredth.The number of unemployed will be 5 in the year Answer Using this tool we find the r-value to be Answer

Answer 1

Let us make a graph for the table. For this graph, we will take the first year (1990) as 0 and each subsequent year by adding 2 to the previous ones

The graph is shown below.

We can see that it is a line graph that slopes downwards.

Hence, the graph is linear.

The model for the graph is given as

`\begin{gathered} y_1\sim ax_1+b \\ \text{where }a=-22.803,b=736.727 \\ y_{}=-22.803x_{}+736.727 \end{gathered}`

Hence, the graph model is

`y_{}=-22.803x_{}+736.727`

What year will number of unemployed reach 5?

We will use the graph model to determine this.

This becomes

`\begin{gathered} y_{}=-22.803x_{}+736.727 \\ So,\text{ here, y = 5. And we will find x} \\ 5_{}=-22.803x_{}+736.727 \\ 22.803x=736.727-5 \\ 22.803x=731.727 \\ x=(731.727)/(22.803) \\ x=32.089 \\ x\text{ is approximately 32} \end{gathered}`

Now, since we took 1990 as 0, the year when the number of unemployed will be 5 becomes

`1990+32=2022`

Hence, the answer is year 2022