The price of fuel may increase due to demand and decrease due to overproduction. emily is studying the change in the price of two types of fuel, a and b, over time.

the price f(x), in dollars, of fuel a after x months is represented by the function below:

f(x) = 2.96(1.04)x

part a: is the price of fuel a increasing or decreasing and by what percentage per month? justify your answer. (5 points)

part b: the table below shows the price g(m), in dollars, of fuel b after m months.

m (number of months) 1 2 3 4
g(m) (price in dollars) 3.04 3.22 3.41 3.61

which type of fuel recorded a greater percentage change in price over the previous month? justify your answer. (5 points)

Part a:

given  where  represents the initial value of the fuel at 0 months. the value  represents the multiplier and the variable  represents the number of months.

the multiplier indicates whether an exponential function growing or decaying. multiplier > 1 indicates growth whereas multiplier < 1 indicates decay.

multiplier 1.04 in this context represents a 0.04 increase which as percentage is 4%

hence,  is an increasing function with 4% compound increase monthtly

part b

as  increases in ones,  increase by the ratio of  (rounded to 2 dp).

the value 1.06 represents increase by 0.06 which as percentage is 6%

hence, the fuel b has a greater percentage monthly increase