Plz Help 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.

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.

Using the exponential regression model given, the answers to the questions given are :

Given the function :

The function represents the exponential decay function since the percentage is less than 1.

The percentage can be obtained thus :

1 - b = 0.82

1 - 0.82 = b

0.18 = b

Hence, the percentage decrease is (0.2 × 100) = 18%

B.)

Using an exponential regression calculator, the data in table 2 can be modeled thus :

Percentage change :

1 - b = 0.56

b = 1 - 0.56

b = 0.44

Hence, the function 2 has the greater percentage change.

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For product A, the product is increasing, for the bigger the number you plug into x (due to the fact that the numbers become bigger because of the time: year 1, year 2, etc)

Product A is 82% change rate, while

product B is 983.45/4 = 245.8625,  1756.16/3 = 585.3867

Product B is 245.8625/585.3867

product B is 42% change rate

Product A change rate is higher than Product B by 40%

Step-by-step explanation:

Hope this helped! :)