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) = 2.15(0.98)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) 4.19 3.98 3.78 3.59
which type of fuel recorded a greater percentage change in price over the previous month? justify your answer. (5 points)

(10 points)

Part A) The price of fuel A is decreasing by a percentage of 2% per month

Part B) Fuel B recorded a greater percentage change price over the previous month (5%) than the Fuel A (2%)

Step-by-step explanation:

Part A: Is the price of fuel A increasing or decreasing and by what percentage per month?

we know that

The equation of the exponential function is equal to

where

x ---> the number of months

f(x) ----> is the price in dollars

a ----> is the initial value or y-intercept

r ---> is the percent rate of change

we have

so

Find the value of r

The rate of change is negative

That means ----> Is a exponential decay function

therefore

The price of fuel A is decreasing by a percentage of 2% per month

Part B) The table below shows the price g(m), in dollars, of fuel B after m months.

we know that

The exponential function is equal to

where

m ---> the number of months

g(m) ----> is the price in dollars

a ----> is the initial value or y-intercept

r ---> is the percent rate of change

Find the value of r

For m=1, g(m)=4.19

substitute

----> equation A

For m=2, g(m)=3.98

substitute

----> equation B

Divide 3.98 by 4.19

simplify

Is negative because is a decreasing function

so

The price of fuel B is decreasing by a percentage of 5% per month

therefore

Fuel B recorded a greater percentage change price over the previous month (5%) than the Fuel A (2%)

wholesale price is the initial price before markup. retail price comes after the markup.

a price of 8 bucks that's marked up by 100%   is

formula: initial price + (percent markup in fraction/decimal)(initial price)

8+(1)(8)

8+8

16

retail price is $16.