Part A:
The average rate of change refers to a function's slope. Thus, we are going to need to use the slope formula, which is:
and 
are points on the function
You can see that we are given the x-values for our interval, but we are not given the y-values, which means that we will need to find them ourselves. Remember that the y-values of functions refers to the outputs of the function, so to find the y-values simply use your given x-value in the function and observe the result:
Now, let's find the slopes for each of the sections of the function:
<u>Section A</u>
<u>Section B</u>
Part B:
In this case, we can find how many times greater the rate of change in Section B is by dividing the slopes together.
It is 25 times greater. This is because 
is an exponential growth function, which grows faster and faster as the x-values get higher and higher. This is unlike a linear function which grows or declines at a constant rate.
Answer:
Step-by-step explanation:
First solve -5x+9y=-12 for x:
-5x+9y=-12
-5x+9y-9y=-12-9y
-5x=-12-9
-5x=-9-12
-5x/-5=-9/5-12/-5
x=9/5y+12/6
Substitute x into an equation
3(-9/5y+12/6)+2y=22
37/5y+36/5=22
37/5y+36/5-36/5=22-36/5
37/5y=74/5
37/5y/37/5=74/5/37/5
y=2
Substitute y in x=-9/5y+12/6
9/5(2)+12/6
x=6
Solution Set: (6,2)
xoxo
Answer:
We can now write this is a function of time in years leading to
f
(
x
)
=
200
(
.94
)
x
f
(
5
)
≈
147
Explanation:
Firs you should consider that if its exponential then it has some form similar to
3
x
. Where we have some known part (3) and the unknown part (
x
) that we are trying to find out. Mathematically we can say it has the form
a
x
. In this case we know what the
a
is and that is the entire population that was given to us. We know over time it will change but why are we even using the exponential model.
Well it turns out that if you multiply some value over and over again it has this form. Example we multiply
2
⋅
2
⋅
2
⋅
2
=
2
4
. So if something doubled over time then this is what would happen.
Now the problem is that it will continue to decrease at the same rate leading to
a
⋅
(
.94
)
because only
94
%
of the population remains each year. After two years
a
⋅
(
.94
)
⋅
(
.94
)
. We can now write this is a function of time in years leading to
f
(
x
)
=
200
⋅
(
.94
)
x
f
(
5
)
≈
147
Step-by-step explanation:
Answer:
82 feet
Step-by-step explanation:
50 feet + 32 feet = 82 feet
Let
X=<span>the original price of the pair of headphones
then
if the % </span>off sale is 40--------------- > (1-0.40)*X=<span>$36
x=36/0.60=60
the answer is
</span>the original price of the pair of headphones was $60
