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

Question

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

If milk costs $4.70 now, what will it cost next year?

If milk costs $4.70 now, how long will it take for the price to top $5?

What type of function did you use to model the scenario? Be specific.

Why did you choose that type of function? What characteristics of the model led you to make that choice?

Did you write a formula for the function? If not, do so now. Be sure to state what the independent and dependent variable represent in the model.

Answer 1

Monica, all problems of this type are progressive in nature, for example

assume we start at the year 2000 with a price = P_o, then at the end of the year 2000, the cost will be

P₁ = P_o(1.0136) then at the end of year 2001 - the second year, the price will be

P₂ = {P_o(1.0136)}(1.0136) = P_o(1.0136)² etc.as you can now see the trend

So, at the end of the nth year, the price will be P_n = P_o(1.0136)ⁿ

You can work all the questions using this general formula!