Question

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)xPart 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)1234f(t) (price in dollars)6584.5109.85142.81Which product recorded a greater percentage change in price over the previous year? Justify your answer. (5 points)

Answer 1

Part A.

According to the given equation, the price of product A is increasing, this is because the number that is being raised to x is greather than 1, which means that each year the price will be greater.

It is increasing by a 25% per year (we know this because the number is 1.25, which means that each year it increases 0.25 of its value).

Part B.

We can use the given values to find the value of the percentage change in price of product B:

$\begin{gathered} 84.5=65(x) \\ \frac{84.5}{65}=x \\ 1.3=x \\ \end{gathered}$

It means that the percentage change in price of product B is 30%. In conclusion, product B has a greater percentage change in its price.