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. (5 points)

Part a: the price of product a increasing by 25% each year. this is because                                                                                             f(x) = 72(1.25)^xis an exponential function with a base of 1.25. suppose that we have a number n. then 25% of n is 0.25n. increasing n by 25% would result in n + 0.25n. factoring out n yields n(1+0.25) = n(1.25), hence multiplying a number by 1.25 increases it by 25%.part b: for product a modeled by f(x), the percent change is 25%. for product b modeled  by f(t), the percent change can be found by                                                        84.5 / 65 = 1.3                                                        109.85 / 84.5 = 1.3                                                        142.81 / 109.85 = 1.3as we can see, the next numbers are obtained by multiplying the previous by 1.3. that means product b has a base of 1.3 and therefore is a 30% increase. the answer is that product b recorded a greater percentage change in price.

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