Question

The price of fuel may increase due to demand and decrease due to overproduction. Emily 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) = 2.96(1.04)*
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) 3.04 3.22 3.41 3.61
Which type of fuel recorded a greater percentage change in price over the previous month? Justify your answer. (5 points)

Answer 1

An exponential function can either represent a growth or decay.

• The price of fuel A is increasing.
• Fuel B recorded a greater percentage change in price

Part A

For fuel A, the exponential function is given as:

$f(x) = 2.96(1.04)^x$

An exponential function is represented as:

$y = ab^x$

Where b represents the rate.

By comparison

$b = 1.04$

Since b (i.e. 1.04) is greater than 1, then the price of fuel A is increasing.

Part B

The table represents an exponential function.

The rate of fuel B is calculated by dividing the current price by the immediate previous price.

So, we have:

$b = \frac{3.41}{3.22}$

$b = 1.06$

By comparison, 1.06 is greater than 1.04 (the rate of fuel A).

Hence, fuel B recorded a greater percentage change in price

Read more about exponential functions at:

brainly.com/question/11464095