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 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. (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) 65 84.5 109.85 142.81 Which product recorded a greater percentage change in price over the previous year? Justify your answer.

Answer 1

We write the function f like this:
$f(x)=72(1+0.25)^x$
It means that the price is increasing by $25\%$ a year. 
B)Let compute the price change of the product B:
$\frac{142.81-109.85}{109.85}\times100=30\%$
We deduce that product B recorded a greater percentage.