Answer:
Product A has a greater percentage change in price.
Step-by-step explanation:
Part A:
The price f product A, f (<em>x</em>) after <em>x</em> years is given by:
After <em>x</em> = 0 years, the price of product A is:
After <em>x</em> = 1 years, the price of product A is:
After 1 year, the price of product A is 3% times more than the original price.
This means that after one year, the new price is 103% of the original price, which means the price product A is increasing by 3%.
Again after <em>x</em> = 2 years, the price of product A is:
This implies that after 2 years, the price of product A is 103% of the price after year 1.
This implies that the price of product A is 3% more than the previous year.
Thus, the price of product A is increasing each year by 3%.
Part B:
The data for Product B is as follows:
Time (t) Price [f (t)]
1 10,100
2 10,201
3 10,303.01
4 10,406.04
Product B is clearly increasing in price.
Consider the changes in price of Product B in the following intervals of years:
- Year 1 - Year 2:
Price in year 1 = $10,100
Price in Year 2 = $10,201
Compute the increase percentage as follows:
- Year 2 - Year 3:
Price in Year 2 = $10,201
Price in year 3 = $10,303.01
Compute the increase percentage as follows:
- Year 3 - Year 4
Price in year 3 = $10,303.01
Price in Year 4 = $10,406.04
Compute the increase percentage as follows:
It is quite clear that the price of product B increases by 1% each year.
Thus, Product A has a greater percentage change in price.