2.
(04.05 mc)
the price of fuel may increase due to demand and decrease due to overproduction. george 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) = 2.27(0.88)^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) 3.44 3.30 3.17 3.04

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

(10 points)

Explanation:

Part A:

The function         calculates the price of fuel A each month by multiplying the price of the month before by 0.88.

Month       price, f(x)

1                 2.27 (0.88) = 1.9976 ≈ 2.00

2                2.27(0.88)² = 1.59808 ≈ 1.60

3                2.27(0.88)³ = 1.46063 ≈ 1.46

Then, the price of fuel A is decreasing.

The percentage per month is (1 - 0.88) × 100 = 12%, i.e. the price decreasing by 12% per month.

Part B.

Table:

m       price, g(m)

1          3.44

2         3.30

3          3.17

4         3.04

To find if the function decreases with a constant ration divide each pair con consecutive prices:

Thus, the price of fuel B is decreasing by (1 - 0.96) × 100 =4%.

Hence, the fuel A recorded a greater percentage change in price over the previous month.

4.6875 pounds

step-by-step explanation: