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) = 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.

Part A.

1) Function given:



2) Interpretation:

initial value: => x = 0 => f(x) = 0.69

table:

x                f(x)
year          price

0              0.69

1             0.69 * 1.03 = 0.7107 => increase = 3%

2             0.69 * (1.03)^2 = 0.732021 => increase = 3%

So, the answer is that the function is increasing at 3% per year.

Part B.

3) table

t (number of years)     1            2             3                 4
f(t) (price in dollars)    10,100   10,201    10,303.01  10,406.04

Percent change:

Year 2: 10,201 / 10,100 = 1.01 => 1% increase

Year 3: 10,303.01 / 10,201 = 1.01 => 1% increase

Year 4: 10,406.04 / 10,303.01 = 1.01 => 1% increase.

the product of the part A recorded a greater percentage change in price over the previous year (3% vs 1%).