Question

2.

Answer 1

Answer:

• Part A: The price of fuel A is decreasing by 12% per month.

• Part B: Fuel A recorded a greater percentage change in price over the previous month.

Explanation:

Part A:

The function     $f(x)=2.27(0.88)^x$     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:

• ratio = 3.30 / 3. 44 = 0.959 ≈ 0.96

• ratio = 3.17 / 3.30 = 0.960 ≈ 0.96

• ratio = 3.04 / 3.17 = 0.959 ≈ 0.96

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.