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) = 2.15(0.98)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) 4.19 3.98 3.78 3.59

Answer 1

Part A: The price of fuel A is decreasing by 2% per month. Part B: The price of fuel B is decreasing by approximately 5% per month.

Step-by-step explanation:

Part A:
To determine whether the price of fuel A is increasing or decreasing, we need to analyze the function f(x) = 2.15(0.98)x. The general form of this function is f(x) = a · rx, where a represents the initial price and r represents the rate of change. In this case, the initial price is 2.15 dollars and the rate of change is 0.98, which is less than 1. Since the rate of change is less than 1, the price of fuel A is decreasing over time. To determine the percentage decrease per month, we can subtract 1 from the rate of change, multiply by 100, and express it as a percentage. In this case, the percentage decrease per month is (0.98 - 1) · 100 = -2%. Therefore, the price of fuel A is decreasing by 2% per month.

Part B:
To analyze the price of fuel B over time, we can observe the given table:

m (number of months)
g(m) (price in dollars)


1
4.19


2
3.98


3
3.78


4
3.59

From the table, we can observe that the price of fuel B is decreasing over time. For example, the price drops from 4.19 dollars to 3.98 dollars from month 1 to month 2. This represents a decrease of 4.99%. Similarly, the price decreases by 4.76% from month 2 to month 3, and by 5.03% from month 3 to month 4. Therefore, the price of fuel B is decreasing by approximately 5% per month.