Profit Function Model Comparison
Two companies start up at the same time. Company A claims their annual profits follow a linear model, P(x) = 10x − 7 where x is the number of units sold and x ≥ 1 . Company B claims that their annual profits follow a radical model, P(x)=15 √ (x − 1) + 3 or P(x) = 15sqrt(x − 1) + 3, where x is the number of units sold and x ≥ 1. It is your job to investigate the validity of each claim.
1. Choose five values for x to plug into the linear function, P(x) = 10x − 7 and create a table of values.
2. Use the same five x values to plug into the radical function, P(x)=15 √ x − 1 + 3 or P(x) = 15sqrt(x − 1) + 3, and create a table of values.
3. Using the table of values from parts 1 and 2 graph both functions. Upload the graph as an attachment to your post, or paste it directly into the DB using the Paste as HTML feature or Picture feature of the toolbar.
4. Using the graphs from part 3 compare the profits of each company and evaluate their claims. Which model seems more realistic, the linear or radical model, and why?
5. Of the function types you have studied so far—linear, quadratic, radical, or rational—which function type is more likely to represent a real profit function for a real company? Give a scenario for a specific type of company, and then give justification for why you chose that function type for that type of company.