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

A: Fuel A is decreasing 2% per month

B: Fuel B is decreasing 5% per month, a greater change

Explanation:

Given the price equation f(x) = 2.15(0.98^x) and a price table for g(m), you want to know the percentage by which f(x) is increasing or decreasing, and if f(x) or g(m) recorded a greater change over the previous month.

(a) Change in f(x)

The function f(x) is of the form ...

f(x) = (initial value)·(growth factor)^(time)

where ...

growth factor = 1 + growth rate

Using this last equation and comparing the function forms, we see ...

growth factor = 0.98 = 1 +growth rate

growth rate = 0.98 -1 = -0.02 = -2%

The price of fuel A is decreasing at 2% per month.

(b) Change in g(m)

The percentage change in g(m) can be found by ...

(g(2) -g(1))/g(1) × 100%

(3.98 -4.19)/4.19 × 100% ≈ -5.0%

The price of fuel B records a greater percentage price change over the previous month.

<95141404393>