The price of products may increase due to inflation and decrease due to depreciation. Marco 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) = 72 (1.25) x

Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer.

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) 65 84.5 109.85 142.81

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

Question

Damon Sexton

Mathematics

Yesterday, 23:52

The price of products may increase due to inflation and decrease due to depreciation. Marco 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) = 72 (1.25) x

Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer.

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) 65 84.5 109.85 142.81

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

+2

Answers (1)

Know the Answer?

Alex Parker · Answer 1

Part A) 25% increase

Part B) Product B

Step-by-step explanation:

Assuming f (x) = 72 * (1.25^x)

At x=0, f (x) = 72 (1.25^0) = 72

At x=1, f (x) = 72 (1.25^1) = 90

Change is 90-72=18

(increases by 18)

Percentage change

= (change/initial) * 100

= (18/72) * 100 = 25%

Product B:

t=1, f (t) = 65

t=2, f (t) = 84.5

Change = 84.5-65 = 19.5 (increase)

Percentage increase

= (19.5/65) * 100

= 30% increase

Product B recorder a greater percentage change (increase)