Example 3

The Gotham Gizmo Company has been rather successful, and has steadily added employees over the past several years. The corporate accountant has noticed that the company’s profit has declined in recent years, so she wants to analyze the relationship between the company’s profit and the number of employees. The data is organized in the following table. What type of model is most appropriate for this data—linear, quadratic, or exponential? Write an equation for this model, and use it to determine the number of employees that will produce the maximum profit.