Question

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 xx years is represented by the function below: f(x)=72×(1.25) ˣ. Is the price of product A increasing or decreasing and by what percentage per year?

A) Increasing by 25%

B) Increasing by 20%

C) Decreasing by 25%

D) Decreasing by 20%

Answer 1

The price of product A is increasing by 25% per year.

Step-by-step explanation:

The price function for product A is given by f(x) = 72 * (1.25)x. To determine whether the price is increasing or decreasing, we need to analyze the exponent, which represents the number of years.

Since the base of the exponent, 1.25, is greater than 1, the function is exponential growth. This means that as the number of years increases, the price of product A will also increase.

Now, let's calculate the percentage increase per year. The rate of growth is given by (1.25 - 1) * 100%, which simplifies to 25%. Therefore, the price of product A is increasing by 25% per year. So, the answer is A) Increasing by 25%.