Question

2.The price of products may increase due to inflation and decrease due to depreciation. Derek is studying the change in the price of two products, A and B, over time.

The price f(x), in dollars, of product A after x years is represented by the function below:

f(x) = 72(1.25)x

Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)

Part B: The table below shows the price f(t), in dollars, of product B after t years:


t (number of years)
1 2 3 4

f(t) (price in dollars)
65 84.5 109.85 142.81


Which product recorded a greater percentage change in price over the previous year? Justify your answer.

Answer 1

You know that this function is DECREASING because 0.63, the number inside of the parenthesis, is LESS THAN THE NUMBER 1. I [think I] know the way to determine by what percentage it is decreasing. [I think] My teacher taught me that I have to subtract the number, in this case 0.63, from 1. So, 1 - 0.63 = 0.37. So it is decreasing by 0.37.

B: Year 1-2 they are all changing by the same percentage: 43% less. And you can prove it by dividing year 2 to year 1 and dividing year 3 to year 2.