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) = 12500(0.82)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) 5600 3136 1756.16 983.45

which product recorded a greater percentage change in price over the previous year? justify your answer. (5 points)

show !

Part A

The price f(x), in dollars, of product A after x years is given by: 
 



this means that:
 
after 0 years, that is for x=0, the price is , the original price

after 1 years, that is for  x=1, the price is 

so after 1 year, the price is 0.82=82/100=82% times 12,500.

This means that after one year, the new price is 82% of the original price, which means the product is depreciated by 18 %.

After 2 years, for x=2, 

, 

that is, after 2 years, the price is 82% of the price after 1 year.

and so on: after each year, the price is 18% less than the previous year.

the price of product A is decreasing each year by 18%.

Part B:

Product B is clearly decreasing in price, 

consider the changes in price in the following intervals of years:

1-2

if           5600 is 100%
then         3136  is (3136/5600) *100%= 56%, 

so in the 1.year, the product depreciated by 44%,

2-3,

(1756.16/3136)*100%=56%

3-4


(983.45/1756.16)*100%=56%


Clearly, the price of product B decreases by 44% each year.

Product B has a greater percentage change in price.

 

A:the price of product A is decreasing each year by 18%.

B:Product B has a greater percentage change in price.