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) = 0.69(1.03)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) 10,100 10,201 10,303.01 10,406.04
which product recorded a greater percentage change in price over the previous year? justify your answer. (5 points)

part a. the general formula for a value in exponential growth is given as:

a = ao (1 + r)^x

where r is the rate of growth of the function.

looking at the given equation, we can say that the price of product a after x years is increasing by a fraction of 0.03 or 3% per year.

part b. we can see that the increase in price is also exponential since the amount increase is not constant. therefore the equation must also be in the form of:

b = bo (1 + r)^x

we use the data in year 2 and 1 to find for the r:

10,201 = 10,100 (1 + r)^1

1 + r = 1.01

r = 0.01

since the growth rate of product b is only 0.01 or 1% per year, therefore product a has greater percentage change in price over the years which is 3% per year.

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