The price of fuel may increase due to demand and 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) = 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.
Part B: The table below shows the price g(m), in dollars, of fuel B after m months.
Graph Below
m (number of months) 1 2 3 4
g(m) (price in dollars) 4.19 3.98 3.78 3.59
Answers
Given : Two types of Fuel Price f(x), in dollars, of fuel A after x months is represented by the f(x) = 2.15 (0.98)ˣ
& type B Data
m (number of months) 1 2 3 4
g(m) (price in dollars) 4.19 3.98 3.78 3.59
To find : Is the price of fuel A increasing or decreasing and by what percentage per month?
Solution:
Fuel A
f(x) = 2.15 (0.98)ˣ
=> Months Price Change %
0 2.15 (0.98)⁰ = 2.15
1 2.15 (0.98)¹ = 2.15 * 0.98 = - 2%
2 2.15 (0.98)²= 2.15 * 0.98² = - 2%
3 2.15 (0.98)³= 2.15 * 0.98³ = - 2%
4 2.15 (0.98)⁴= 2.15 * 0.98⁴ = - 2%
price of fuel A is decreasing by 2 %
price of fuel A is decreasing and by 2% per month
Fuel B
Months Price Change %
1 4.19
2 3.98 ≈ -5 %
3 3.78 ≈ -5 %
4 3.59 ≈ -5 %
5 % > 2 %
Fuel type B recorded a greater percentage change in price over the previous month
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