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) = 2.96(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 that the growth factor of x (the number of months) is a positive number larger than 1, we have that as the number of months increases, the price of fuel also increases

Therefore, the price of fuel A is increasing, by 4% each month

Part B:

Fuel B records a greater percentage change in price over the previous month.

Step-by-step explanation:

The function that represents the price of fuel A is f(x) = 2.96(1.04)ˣ

Where;

x = The number of months

Part A: Given that the growth factor of x (the number of months) is a positive number larger than 1, we have that as the number of months increases, the price of fuel also increases

Therefore, the price of fuel A is increasing

(2.96(1.04)² - 2.96(1.04)¹)/(2.96(1.04)¹) × 100 = 4 %

(2.96(1.04)³ - 2.96(1.04)²)/(2.96(1.04)²) × 100 = 4 %

(2.96(1.04)⁴ - 2.96(1.04)³)/(2.96(1.04)³) × 100 = 4 %

Part B: The given table is presented as follows;

Months, m                                 The price of fuel, g(m)

1                                                   3.04

2                                                  3.22

3                                                   3.41

4                                                   3.61

The percentage change in price for fuel A over the previous month is given as follows;

Fuel price of fuel A in the previous month f(3) = 2.96(1.04)³≈ $3.33

Fuel price of fuel A in the current month f(4) = 2.96(1.04)⁴ ≈ $3.463

The percentage change in price = (3.463 - 3.33)/3.33 × 100 ≈ 4 % change

The percentage change in price for fuel B over the previous month is given as follows;

Fuel price of fuel B in the previous month = $3.41

Fuel price of fuel B in the current month = $3.61

The percentage change in price = (3.61 - 3.41)/3.41 × 100 ≈ 5.865 % change

Therefore, fuel B recorded a greater percentage change in price of 5.865 %, over the previous month than fuel A with a percentage change in price of 4 %

Fuel B records a greater percentage change in price over the previous month.

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step-by-step explanation:

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0