Question

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. (5 points)

I've been stuck on this all day :-(

Answer 1

I think you have a very fundamental typo.
We are talking about a constant rate of inflation here
I bet you mean
f(x) = 0.69 (1.03)^x
in other words TO THE POWER x
that would be 0.69 when x = 0 years, now
0.69 * 1.03 after one year
0.69 * 1.03 *1.03 after two years
0.69 *1.03*1.03*1.03 after 3 etc

It is getting bigger. Every year you increase by .03 x which is 3%

Answer 2

In your table in part B
the ratio is for example
10406.04/10303.01
= 1.01
check:
10303.01/10201 = 1.01 sure enough
so that is increasing by ONLY ONE percent per year

Answer 3

thank you so much this has helped me so much because i was stuck on this question for some time.