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.

Question

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

f(x) = 0.69(1.03)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) 10,100 10,201 10,303.01 10,406.04

Which product recorded a greater percentage change in price over the previous year? Justify your answer. (5 points

Answer 1

.69*1.03 = .7107
f(x) = .7107 x
so decreasing, depreciation wins

1-.7107 = .2893
so value decreasing by about 29% per year
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in 3 years
(10406.04 -10,100)/4 = 102 increase/year
102/10100 * 100 = 1.01 percent increase per year