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%)

step-by-step explanation:

∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. formed with the point d(1, 2) as its third vertex, then ∆abd is triangle.

answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)