Question

PLEASE HELP FAST 50 POINTS

please ignore the "-14.32"

Answer 1

A) The price of fuel A is decreasing by 5 percent each month.

B) The price of fuel B is decreasing by 4 percent each month.

C) Fuel A

Explanation:

Part A

To calculate the percentage change for fuel A per month, we can use the provided Percentage Change Formula:

`\boxed{\textsf{Percentage Change Formula} = \frac{\textsf{Old Number - New Number}}{\textsf{Old Number}}* 100}`

Calculate the percentage change between consecutive months by substituting the given values into the formula, and rounding to the nearest percent:

`\textsf{Month 1 to 2:}\quad \textsf{Percentage Change}=(4.19-3.98)/(4.19)* 100\approx 5\%`

`\textsf{Month 2 to 3:}\quad \textsf{Percentage Change}=(3.98-3.78)/(3.98)* 100\approx 5\%`

`\textsf{Month 3 to 4:}\quad \textsf{Percentage Change}=(3.78-3.59)/(3.78)* 100\approx 5\%`

So, the price of fuel A is decreasing by approximately 5 percent each month.

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Part B

The price f(x), in dollars, of fuel B after x months is represented by the function:

`f(x)=2.12(0.96)^x`

This is an exponential decay function, in the form f(x) = a(1 - r)ˣ, where "a" is the initial value and "r" is the percentage decrease in decimal form.

Therefore, to calculate the percentage decrease for fuel B, we can set (1 - r) equal to 0.96, and solve for r:

`1 - r = 0.96`

`r = 1 - 0.96`

`r = 0.04`

`r=4\%`

Therefore, the price of fuel B is decreasing by 4 percent each month.

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Part C

Comparing the percentage changes, fuel A is decreasing by approximately 5% each month, while fuel B is decreasing by 4% each month. Therefore, fuel A recorded a greater percentage change.