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


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

Answer 1

Answer:Given :  Two types of Fuel  Price f(x), in dollars, of fuel A after x months is represented by the f(x)  = 2.27 (0.88)ˣ   & type B Data given

To find : Is the price of fuel A increasing or decreasing and by what percentage per month?

Solution:

Fuel A

f(x)  = 2.27 (0.88)ˣ

=> Months       Price                                                   Change %

     0               2.27 (0.88)⁰ = 2.27

     1                2.27 (0.88)¹ = 2.27  * 0.88                  = -12%

     2                2.27 (0.88)²= 2.27  * 0.88²                = -12%

     3                2.27 (0.88)³= 2.27  * 0.88³                = -12%          

     4                2.27 (0.88)⁴= 2.27  * 0.88⁴                = -12%    

price of fuel A  is decreasing by 12 %

Fuel B

Months            Price                 Change %

1                        3.44

2                       3.30                    ≈ -4 %

3                       3.17                    ≈ -4 %

4                       3.04                  ≈ -4 %

12 % > 4 %

Fuel type A  recorded a greater percentage change in price over the previous month