Question

Modeling with Functions

In this course you have learned the characteristics of different types of functions and have practiced solving application problems involving 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 in writing the function to model the situation. Be sure to state what the independent variable represents. Then use your model to answer the questions for that scenario.

1. The price of a gallon of milk has been rising about 1.36% per year since 2000.

   1. What type of function would be best to model this scenario? Choose one of the following: linear, quadratic, polynomial of degree 3 or higher, rational, exponential, or logarithmic. Explain why you chose this answer.

   2. Write a formula for the function you chose to model this scenario. What does the independent variable in your function represent?

   3. If milk costs $4.70 now, what will it cost next year? Show how you found the answer.

   4. If milk costs $4.70 now, how long will it take for the price to top $5? Show how you found the answer.

Answer 1

(a) Linear equation (b) A = P(1 + R/100) ^T (c) A = $ 4.76 (D) T = 5 Years