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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) = 2.27(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.



Answer :

sqdancefan

Answer:

  A. decreasing 12% per month

  B. fuel A recorded the greater change

Step-by-step explanation:

Given an equation and a table of values, you want to compare the rates of change each represents.

A.

The fuel price is described by ...

  f(x) = 2.27(0.88^x)

We recognize this exponential equation to be of the form ...

  f(x) = (initial value) × (growth factor)^x

Comparing parts of the equation, we see ...

  growth factor = 0.88

The relation between growth factor and growth rate is ...

  growth factor = 1 + growth rate

  growth rate = growth factor - 1 = 0.88 -1 = -0.12 = -12%

This tells us the rate of change in fuel price is -12% per month.

B.

To find the percentage change, we can use the formula ...

  percent change = ((new value) / (old value) -1) × 100%

Applied to the first two table values, we have ...

  percent change = (3.30/3.44 -1) × 100% ≈ -4.07%

This decrease of 4.07% is less than the decrease of 12% represented by the equation. Type A fuel recorded the greater percentage change.

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