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)
Answers
Answer:
Step-by-step explanation:
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