Answers
Answer:
a) The average rate of change for the function [tex]f(x)=4(2)^x[/tex] over interval x=1 to x=2 is 8
b) The average rate of change for the function [tex]f(x)=4(2)^x[/tex] over interval x=3 to x=4 is 32
Step-by-step explanation:
We are given function [tex]f(x)=4(2)^x[/tex]
We need to find Average rate of change
The formula used is: [tex]Average \ rate \ of \ change=\frac{f(b)-f(a)}{b-a}[/tex]
Part a) The interval is: x=1 to x=2
We have a= 1 and b=2
Finding f(a) i.e f(1)
[tex]f(x)=4(2)^x\\Put \ x =1\\f(1)=4(2)^1\\f(1)=4(2)\\f(1)=8[/tex]
Now finding f(b) i.e f(2)
[tex]f(x)=4(2)^x\\Put \ x =2\\f(2)=4(2)^2\\f(2)=4(4)\\f(2)=16[/tex]
Now finding average rate of change.
[tex]Average \ rate \ of \ change=\frac{f(b)-f(a)}{b-a}\\Average \ rate \ of \ change=\frac{16-8}{2-1} \\Average \ rate \ of \ change=\frac{8}{1}\\Average \ rate \ of \ change=8[/tex]
So, average rate of change for the function [tex]f(x)=4(2)^x[/tex] over interval x=1 to x=2 is 8
Part b)
The interval is: x=3 to x=4
We have a= 3 and b=24
Finding f(a) i.e f(3)
[tex]f(x)=4(2)^x\\Put \ x =3\\f(3)=4(2)^3\\f(3)=4(8)\\f(3)=32[/tex]
Now finding f(b) i.e f(4)
[tex]f(x)=4(2)^x\\Put \ x =4\\f(4)=4(2)^4\\f(4)=4(16)\\f(4)=64[/tex]
Now finding average rate of change.
[tex]Average \ rate \ of \ change=\frac{f(b)-f(a)}{b-a}\\Average \ rate \ of \ change=\frac{64-32}{4-3} \\Average \ rate \ of \ change=\frac{32}{1}\\Average \ rate \ of \ change=32[/tex]
So, average rate of change for the function [tex]f(x)=4(2)^x[/tex] over interval x=3 to x=4 is 32
Since the interval is increasing, so does our average rate of change increasing as function is also increasing.
Related Questions
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Answers
Answer:
2/3 / 1/6
4/6 / 1/6
1/6 can go into 4/6 4 times. the answer is C; 4
Step-by-step explanation:
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Answer:
your answer will be $29.
1 LB= $4
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Which one should I choose
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Answer:
C. 10x^2
Step-by-step explanation:
Which factor is least likely to affect the results and interpretation of a functional MRI?
A. cancerous growth
B. prescription medication
C. a sinus infection
D. caffeinated soda
Answers
Answer:
Cancerous growth
Step-by-step explanation:
For example, a tumor would be found in MRIs and will have a significant impact on the results and interpretation of a functional MRI. A tumor that is cancerously growing is very crucial to the function of an MRI
I hope this helps
The functional MRI also known as fMRI monitors brain anatomy activity
The factor that is least likely to affect the results and interpretation of a
functional MRI is; C. A sinus infection.
Reasons:
MRI stands for magnetic resonance imaging, and it is used to generate
images of the interior of items, such as the human body, without opening
the body, by producing strong magnetic fields, from the built in powerful
magnets.
The parts of the body that are examined by an MRI scan includes, the
internal organs, blood vessels, brain, and spinal cord.
The MRI scan works by tracking radio signals sent by protons in the body
which vary based on the type of tissue.
Due to the requirement for the patient to remain stationary during the
scan, medication may be given. It is also important to not take caffeinated
drinks prior to the examination.
A functional MRI is used to monitor the functioning of the brain's anatomy,
by blood flow change detection.
Therefore, the factor that is least likely to affect the result and
interpretation of a functional MRI is a sinus infection which is the
inflammation of the sinus lining and mucus presence, that rarely cause
neurologic complications.
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Answers
Answer:
it is 15
Step-by-step explanation:
Answer:52
Step-by-step explanation:
In a scale drawing 1/2 inch represents 3 feet. If the same scale is used, how many inches will be needed to represent 24 feet?
2 inches
4 inches
8 inches
12 inches
Answers
Since 24/3 = 8
Multiply 1/2 by 8
1/2 * 8 = 4
Identify the parent function and describe the transformation of the equation y=2〖(x+5)〗^3-4
Answers
Answer:
2x - 6 = 5x-10 ... 4. 2x-1= x - 5+ 3x. 2x-1=4x-5. - +5 +5. 5. 3(y-1)=-(4-5). 3y-3 = -4+5. +y
Step-by-step explanation:
ALL I NEED IS #9 PLS
Answers
Answer:
x=24
Step-by-step explanation:
x/6=4
4*6=x
x=24
Michael’s home is 12 feet below sea level and his mother’s home is 12 feet above sea level. Michael says their homes are at opposite elevations because they are in opposite directions. Is he correct? Explain.
Answers
Answer:
Yes he is correct because -12 and 12 are the opposite.
Step-by-step explanation:
Answer:
He is correct because the numbers are in opposite directions on the number line, and their distances from 0 on the vertical number line are equal
y = 4x + 2
y= x2 + 6x + 5
Answers
Answer:
im sorry for doing this but i really need points
Step-by-step explanation:
Can you help me with this math problem? Im having a hard time with it, if you can explain it too that would help a lot. attachment below
Answers
Answer:
[tex]3^{-3}\cdot \:\:8^{-3}=\frac{1}{24^3}[/tex]
Thus, the equivalent expression is: [tex]\frac{1}{24^3}[/tex]
Step-by-step explanation:
Given the expression
[tex]3^{-3}\cdot 8^{-3}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}[/tex]
[tex]=8^{-3}\cdot \frac{1}{3^3}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}[/tex]
[tex]=\frac{1}{3^3}\cdot \frac{1}{8^3}[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}[/tex]
[tex]=\frac{1\cdot \:1}{3^3\cdot \:8^3}[/tex]
[tex]=\frac{1}{24^3}[/tex]
Thus,
[tex]3^{-3}\cdot \:\:8^{-3}=\frac{1}{24^3}[/tex]
Thus, the equivalent expression is: [tex]\frac{1}{24^3}[/tex]
What is the correct equation to solve for x? Help
Answers
Answer:
tan (46°) = 17/x
Step-by-step explanation:
tan (46°) = 17/x
Answer:
tan(46) = 17/x
Step-by-step explanation:
The tangent of an angle is opposite over adjacent, so the tangent of 46 is 17/x, not x/17. Also, sin(46) = opposite/hypotenuse and cos(46) = adjacent/hypotenuse, but we aren’t given the hypotenuse. Therefore, the answer has to be tan(46) = 17/x.
Describe, with examples of your own, when you would use long division and synthetic division and how to check polynomial division.
Answers
GIVEING BRAINLIST PLZ HELP On the number line, a point was moved from -7 to -3. Which of the following problems describes this move?
-7 + 3 = -4
-7 - 4 = -3
-7 - 3 = -10
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Answers
Answer:
c
Step-by-step explanation:
Find the 69th term of the following arithmetic sequence.
18, 25, 32, 39,
Answers
Answer:
18+68(25-18)=18+68(7)
=18+476
=494
What is the answer to this?
Answers
Answer:THE ANSWER IS C HOPE THIS HELPS ANY
Step-by-step explanation:
what is y=2x can someone pleas help me
Answers
Answer:
Slope: 2
Step-by-step explanation:
Answer:
x=y/2
Step-by-step explanation:
you divide 2 from both sides then you get y/2
When a regression line was used to model exponential data, the -value was
0.668. If the data are linearized using logarithms and then modeled again
with a regression line, the value will be greater than 0.668.
OA. True
OB. False
Answers
The statement about the correlation coefficient of the exponential and logarithmic model is true
How to determine the true value of the statement?The correlation coefficient, r² is given as:
r² = 0.668
An exponential model and a logarithm model are inverse functions.
This means that, their correlation coefficients are also inverse
Given that the correlation coefficient, r² of the exponential data is 0.668.
And the highest value of the correlation coefficient is 1.
This means that the correlation coefficient, r² of the logarithmic data would be less than 0.668
Hence, the given statement is true.
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Answer:
true
Step-by-step explanation:
You bought a house in 1963 for $56,000. Since then, you have increased the value 6% per year. What is the value of your house in 2017?
Answers
Answer:
244,160
Step-by-step explanation:
Help pleaseeee cxxxcxx
Answers
Answer:
no. I'm pretty sure it's not
There are 4 red apples and 3 green apples. How many red and green apples are there?
Answers
Answer:
7
Step-by-step explanation:
Just add them together...
In the figure below, lines p and s are parallel.
Answers
Answer:
c
Step-by-step explanation:
i used a calculator (they never lie)
Answer:
22
Step-by-step explanation:
60+6x-12= 180
6x = 180 -48
x= 132/6= 22
translate the unit 3 units right and 7 units down what will the new coordinate for C be if A(-4,-5) and B(0,1)
Answers
Answer:
After the transition, point A is at Location (-1, -12) and point B is located at (-2, 7)
Step-by-step explanation:
hope that helps
Let V(t) represent the value of a bank account, in thousands of dollars, t years after the account is opened at the bank. Determine whether each statement below is true. Select True or False for each statement.
V(0) = 2 means that the value of the bank account when it is opened is $2000
V(5) = 2.2 means that 2.2 years after the bank account is opened, its value is $5000
V(10) – V(5) = 0.4 means that the bank account grows by $400 between 5 and 10 years after its opening
Answers
Answer:
True false false
Step-by-step explanation:
The following statements can be considered true or false as the case may be as follows;
V(0) = 2 means that the value of the bank account when it is opened is$2000 --TRUEV(5) = 2.2 means that 2.2 years after the bank account is opened, its value is $5000 --FALSEV(10) – V(5) = 0.4 means that the bank account grows by $400 between 5 and 10 years after its opening --TRUEDiscussion:
The function takes the form;
V(t) = Value of account.Ultimately,
Statement 1 is true; Statement 2 is false; andStatement 3 is true.Read more:
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Lashonda is saving money to buy a game. So far she has saved $6, which is two-thirds of the total cost of the game. How much does the game cost?
Answers
Answer:
The game costs $9
Step-by-step explanation:
I wrote an equation using the variable "t" for the total cost of the game.
6=2/3t
t=6/2/3
t=(6/1)(3/2)
t=18/2
t=9
Lots a Loot Bank charges a monthly service fee and a fee per check, and the chart below shows your total monthly fees in relation to the number of checks issued per month.
Answers
Answer:
Monthly service fee is like the fixed cost which is basically the y-value where graph crosses the y-axis.
From graph we see that graph crosses at 1 on y-axis so monthly service fee according to sample graph = $1
Now the per check fee works like slope of the line.
To find the slope we need two points so find any two points on the graph of line. I'm using points (1,0) and (4,3)
now slope can be found using formula
Hence per check fee will be $0.5 as per attached sample graph.
You can use same technique for the original graph given with this question.
Step-by-step explanation:
Answer:
A monthly service fee of 0.50 and a per-check fee of 0.50
Step-by-step explanation:
Math question angles
Answers
Answer:
m∠1 = 52°
m∠2 = 38°
Step-by-step explanation:
x + 33 + 2x = 90
3x = 57
x = 19
m∠1 = 19 + 33 = 52°
m∠2 = 2 ( 19 ) = 38°
do two lines that intersect make 4 right angles
Answers
Answer:
if they are perpendicular
Answer:
Yes
Step-by-step explanation:
Two lines that intersect each other can intersect each of perpendicularly, which forms 4 right angles.
I hope this helps!
question
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Answers
Answer:
32 and 5n + 2
Step-by-step explanation:
(a)
The pattern of the number of sticks is
7, 12, 17
There is a common difference of 5 between consecutive terms.
Thus to obtain the number of sticks in number 6 , add 5 to previous terms, that is
a₄ = 17 + 5 = 22
a₅ = 22 + 5 = 27
a₆ = 27 + 5 = 32
There are 32 sticks in pattern number 6
(b)
The sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
Where a₁ is the first term and d the common difference
Here a₁ = 7 and d = 5 , then
[tex]a_{n}[/tex] = 7 + 5(n - 1) = 7 + 5n - 5 = 5n + 2
number of sticks in pattern number n is 5n + 2
32 and 5n + 2
Step-by-step explanation:
(a)
The pattern of the number of sticks is
7, 12, 17
There is a common difference of 5 between consecutive terms.
Thus to obtain the number of sticks in number 6 , add 5 to previous terms, that is
a₄ = 17 + 5 = 22
a₅ = 22 + 5 = 27
a₆ = 27 + 5 = 32
There are 32 sticks in pattern number 6
(b)
The sequence is arithmetic with n th term
= a₁ + (n - 1)d
Where a₁ is the first term and d the common difference
Here a₁ = 7 and d = 5 , then
= 7 + 5(n - 1) = 7 + 5n - 5 = 5n + 2
number of sticks in pattern number n is 5n + 2
Write an equation for the parabola that passes through (1,12) and has vertex (10,-4)
Answers
Answer:
y + 4 = (16/81)(x - 10)
Step-by-step explanation:
The general formula for a parabola passing through (x, y) and with vertex (h, k) is y - k = a(x - h)^2.
Here we are told that x = 1, y = 12, h = 10 and k = -4, which gives us:
12 + 4 = a(1 - 10)^2, or
16 = 81a
Then a = 16/81, and the desired parabola is
y + 4 = (16/81)(x - 10)