Question

The price of fuel may increase due to demand and decrease due to overproduction. Marco 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) = 2.27(0.88)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) 3.44 3.30 3.17 3.04


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

Answer 1

Part A: The price of fuel A is decreasing. The function f(x) is in the form f(x) = ab^x, where a is the initial value and b is the rate of change. In this case, a is 2.27 and b is 0.88. Since b is between 0 and 1, this indicates that the price of fuel A is decreasing over time.

To find the percentage change per month, we can subtract the rate of change (b) from 1 and multiply by 100%. This gives us the formula for finding the percentage change per month: (1 - b) * 100%.

Plugging in the values from the given function, we get: (1 - 0.88) * 100% = 12% decrease per month.

Part B: To find the percentage change in price for each month, we can subtract the price for each month from the price for the previous month and divide by the previous month's price. This will give us the percentage change in price for each month.

m (number of months) 1 2 3 4

g(m) (price in dollars) 3.44 3.30 3.17 3.04

% change -3.85% -4.04% -4.15%

The percentage change in price for fuel B decreases as the number of months increases, indicating that the price of fuel B is decreasing over time. The greatest percentage change in price over the previous month is -4.04%, which occurred between months 2 and 3. Therefore, fuel B recorded a greater percentage change in price over the previous month compared to fuel A.