Modeling with Functions
In this course you have learned the characteristics of differenttypes of functions and have practiced solving application problemsinvolving modeling with these functions. For each scenario below,decide what type of function would best model the situation.Explain why you chose that type of function. Show your work inwriting the function to model the situation. Be sure to state whatthe independent variable represents. Then use your model to answerthe questions for that scenario.
Susan decides to take a job as a transcriptionist so that shecan work part-time from home. To get started, she has to buy acomputer, headphones, and some special software. The equipment andsoftware together cost her $1000. The company pays her $0.004 perword, and Susan can type 90 words per minute.
What type of function would be best to model this scenario?Choose one of the following: linear, quadratic, polynomial ofdegree 3 or higher, rational, exponential, or logarithmic. Explainwhy you chose this answer.
Write a formula for the function you chose to model thisscenario. What does the independent variable in your functionrepresent?
How many hours must Susan work to break even, that is, to makeenough to cover her $1000 start-up cost? Show how you found theanswer.
If Susan works 4 hours a day, 3 days a week, how much will sheearn in a month? Show how you found the answer.
