Question

The local theater puts on an annual play. The tablebelow shows the number of auditions for the lead roleeach year since 2004. Using an equation to model thedata, approximate the number of auditions that willbe held in 2013.

Answer 1

We are asked to model the given data using an equation.

Let us perform the regression analysis to find the equation of the form

`y=mx+b`

Where y is the number of auditions, x is the year, m is the slope, and b is the intercept.

Enter the data into Desmos.

We get the following results

Slope: m = 3.71

Intercept: b = -7422.86

So, the equation of the model is

`y=3.71x-7422.86`

Now, let us approximate the number of auditions that will be held in 2013.

Substitute x = 2013 into the above equation

`\begin{gathered} y=3.71(2013)-7422.86 \\ y=7468.23-7422.86 \\ y=45 \end{gathered}`

Therefore, the approximate number of auditions that will be held in 2013 is 45

Here is the scatterplot with the line of best fit.