Exercise 48 Page 217

We are given a model for the number of students (in thousands) enrolled in public schools. We are asked to use calculator to draw the graph of this model. We begin by pushing the $\boxed{\text{Y=}}$ button and typing the equation of $S$ in the first row.

To see the graph you will need to adjust the window. The given model is valid for $0\le x\le 41,$ so let's use these values as horizontal bounds. Push $\boxed{\text{WINDOW}},$ change the settings, and push $\boxed{\text{GRAPH}}.$

We can see that the graph is increasing, then decreasing, then increasing again. To find the maximum point on the graph, push $\boxed{\text{2nd}}$ and $\boxed{\text{TRACE}}$ and choose maximum from the menu. The calculator will prompt you to choose a left and right bound and to provide the calculator with a best guess of where the maximum might be.

You can find the minimum point similarly.

Let's interpret the result we get on the calculator screen.

• Variable $x$ represents time, so the first coordinate of the turning points gives the time when the trend is changing.
• Variable $y$ represents the number of students on the calculator, so the second coordinate of the turning points gives the number of students when the trend is changing.

The number of students enrolled in public schools is:

• increasing in the first $12$ years and reaches $44971$ thousands,
• then decreasing until year $30$ (so in the next $18$ years) and reaches $40078$ thousands.
• It is then increasing again until year $41,$ which is the last year when the model is valid.