Answers
Given:
The table of values of an exponential function.
To find:
The function for the given table of values.
Solution:
The general exponential function is:
[tex]y=ab^x[/tex] ...(i)
Where, a is the initial value and b is growth factor.
From the given table it is clear that the function passes through the points (1,9) and (2,36). It means the function must be true for these two points.
[tex]9=ab^1[/tex] ...(ii)
[tex]36=ab^2[/tex] ...(iii)
On dividing (iii) by (ii), we get
[tex]\dfrac{36}{9}=\dfrac{ab^2}{ab}[/tex]
[tex]4=b[/tex]
Putting [tex]b=4[/tex] in (ii), we get
[tex]9=a(4)^1[/tex]
[tex]\dfrac{9}{4}=a[/tex]
Putting [tex]a=\dfrac{9}{4},b=4[/tex] in (i), we get
[tex]y=\dfrac{9}{4}(4)^x[/tex]
[tex]y=9(4)^{x-1}[/tex]
The function notation with variable n is:
[tex]f(n)=9(4)^{n-1}[/tex]
Therefore, the correct option is D.
Related Questions
A manufacturer claims that its new hand sanitizer reduces the number of days an average person is sick in a year. To test this claim, a researcher decided to conduct an experiment. The researcher randomly selected 300 people, divided into subject groups by age. Over the course of a year, all the subjects regularly used the hand sanitizer. At the end of the year, the researcher compared the number of days that the subjects in each group were sick.
Which statements about this experiment are true?
Answers
Answer:
The study uses blocking and random sampling.
Step-by-step explanation:
The statement with respect to the experiment should be true is that The study uses blocking and random sampling.
What is random sampling?It should be the part of the technique related to sampling where each and every sample should contain equivalent probability of being selected. The sample that should be selected on random basis should be mean to be non-biased with respect to the total population.
hence, The statement with respect to the experiment should be true is that The study uses blocking and random sampling.
Learn more about experiment here: https://brainly.com/question/9882283
can someone please help me find x
Answers
Answer:
[tex]2\sqrt{5}[/tex]
Step-by-step explanation:
The picture (attached) shows two isosceles right triangles, so the altitude marked x splits the bottom side in half, 4 units and 4 units.
Each triangle is a right triangle with one leg of length 4, hypotenuse 6. Use the Pythagorean Theorem (leg)^2 + (leg)^2 = (hypotenuse)^2.
[tex]4^2+x^2=6^2\\16+x^2=36\\x^2=20\\x=\sqrt{20}\\x=2\sqrt{5}[/tex]
Work out the probability that the spinner will land on 3
Answers
Answer:
https //ryan group.topper.school/ login
The answers to these questions please
Answers
Answer:
Q10 is 13.64 cm3
Q 11 is 221 cm3
Step-by-step explanation:
volume is cross sectional area times height for Q 10
volume is length times width times height for Q 11
Triangle GHI is similar to triangle JKL. Find the measure of side JK. Round your
answer to the nearest tenth if necessary.
I
L
7
33
4
H
K
Answer:
Answers
Answer:
JK = 18.8
Step-by-step explanation:
7/33 = 4/JK
132 = 7JK
JK = 18.86
Answer:
JK=18.8
Step-by-step explanation:
so we are given that ΔGHI ~ ΔJKL
GI~JL (because corresponding parts of similar triangles are similar)
so GI/JL=ratio of similitude=7/33
GH~JK (corresponding parts of similar triangles are similar)
and GH/JK=ratio of similitude
so:
GH/JK=GI/JL
subsitute known values
4/JK=7/33
cross multiply
7JK=132
divide
JK=132/7
simplify and round
JK≈18.8
hope this helps!
Which points are a solution to the graph
Answers
Answer:
3,2
Step-by-step explanation:
Segment AB, with endpoints A(-6,9) and B(12, -3), is dilated by a scale factor of 2/3 centered at the origin.
What are the coordinates of A'?
Enter your answer as an ordered pair, using parentheses and a comma, like this: (42,53)
Answers
The coordinates of A' after the dilation is (-4,6)
How to determine the coordinates of A'?The given parameters are:
A = (-6,9)
B = (12, -3)
Scale factor, k = 2/3
The coordinates of A' is then calculated as:
A' = A * k
This gives
A' = (-6,9) * 2/3
Evaluate the product
A' = (-4,6)
Hence, the coordinates of A' after the dilation is (-4,6)
Read more about dilation at:
https://brainly.com/question/3457976
Cuál es el problema actual que están viviendo los emprendedores?
Answers
Answer:
Los emprendedores se enfrentan a muchos desafíos en el mundo empresarial ultracompetitivo de hoy. Afortunadamente, los emprendedores también tienen más recursos que nunca para abordar esos problemas.
Hoy en día, muchos emprendedores enfrentan los siguientes 10 desafíos. Quizás ya te hayas enfrentado a algunos de ellos. Siga leyendo para saber por qué existe cada desafío y para obtener soluciones y soluciones para que pueda operar su negocio de manera eficiente y exitosa.
Find the missing angle measure.
52
Answers
Answer:
128
Step-by-step explanation:
Sum of interior angles of a 4 sided quadrilateral is 360.
90 + 90 + 52 + x = 360
232 + x = 360
x = 360 - 232
x = 128
14. The table shows the survey results of exercises
people do regularly.
Which is true based on the table?
Answers
Answer:
Answers in the question are A, B, and E.
The answers to the table are:
yes no total
yes: 12 25 37
no: 12 6 18
total: 24 31 55
Hopefully this helped, sorry if I was too late :)
I need a clear answer fast please!!
A movie-theater employee notes an inverse relationship between the theater's popcorn sales
and its nacho sales. On a given night, the theater makes 990 from popcorn sales and
$1,892 from nacho sales. If on the next night the employees sell $1,452 of popcorn, how
much is earned from nachos?
Answers
3(2z + 3)
= -75
I need help ty
Answers
Answer:
= − 1 4
Step-by-step explanation:
Answer:
z = - 14
Step-by-step explanation:
Solving for z using basic algebra
3(2z + 3) = -75
Step 1 distribute the 3
3 * 2z = 6z
3 * 3 = 9
now we have 6z + 9 = -75
step 2 subtract 9 from each side
9 - 9 cancels out
-75 - 9 = -84
now we have 6z = - 84
step 3 divide each side by 6
6z / 6 cancels out
-84 / 6 = -14
we're left with z = -14
Determine whether the set of lengths could form a triangle.
5, 2, and 3.
Answers
Answer:
Determine whether the set of lengths could form a triangle 5, 2 and 3. No it can not form a triangle.
Step-by-step explanation:
5 + 2 is greater than 3. 5 + 3 is greater than 2. 3 + 2 is not greater than 5
Answer:
No, the set of lengths - 5, 2 and 3 will not form a triangle.
Step-by-step explanation:
As we know,
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
[tex]5 + 2 > 3[/tex]
[tex]3 + 5 > 2[/tex]
[tex]2 + 3 = 5[/tex]
Therefore,
it does not satisfy the statement.
is 10x-5=8x-2x + 7 -2 equivalent?
Answers
Answer:
2.5
Step-by-step explanation:
Lets simpify one side first
8x - 2x + 7 +2
8-2 = 6
so 6x
7-2 = 5
6x+9
10x - 5 = 6x +5
(You add 5 due to it being negative on the other side)
+5 +5
10x= 6x +10
-6x -6x
4x = 10
Divide each side by 4
x = 2.5 or 10/4 or 5/2
Answer: No
Step-by-step explanation: To find whether these are equivalent, we first need to simplify the equation on the right.
8x-2x+7-2
8x-2x+5 (work- 7-2 = 5)
6x+5 (work- 8x-2x=6x) These are like terms, so we can subtract them
now that we have simplified, let's write the equations once again.
10x-5=6x+5
they are surely not equivalent
Please Help me with this question will mark as Brainllest
Answers
Answer:
it is 72
Step-by-step explanation:
a pizza has a radius of 2.5 feet what is the circumference of the pizza
Answers
_________________ please help!!!!!!!
Answers
Answer:
The answer would be C)5
Step-by-step explanation:
The unknown triangle is half of the size of the original triangle, The right side measurement basically hints to the actual answer.
What is the standard form of the nymber 6.7321 * 108?
A. 6,732,100,000
B. 673,210,000
C. 67,321,000
D. 6,732,100
Answers
Answer:
673,210,000
Step-by-step explanation:
The given number is :
N = 6.7321 × 10⁸
We need to write it into the standard form.
10⁸ = 100000000
It can be calculated as follows :
6.7321 × 100000000 = [tex]\dfrac{67321 }{10000}\times 100000000[/tex]
= 673,210,000
So, the standard form of the given number is 673,210,000. Hence, the correct option is (c).
Rewrite 8*8*8*8 using an exponent
Answers
Answer:
8⁴
Step-by-step explanation:
8*8*8*8 =8⁴
8 exponent 4
Answer:
[tex]8^{4}\\[/tex]
Step-by-step explanation:
An exponent describes how many times the base is repeatedly shown. For instance:
6³
6 is the base and 3 is the exponent. Because the exponent is 3, the base is repeated that many times. Here's what I mean:
6² = 6 (6) (6)
So in 8 (8) (8) (8), the base would be 8 and this is repeated 4 times. So the exponent would be 4.
So your answer would look like [tex]8^{4}[/tex].
Please help me is this correct ??????
Answers
No it is not correct.
69420-69420x69420+69420-69420 69420-69420x69420+69420-69420
Answers
Answer:
0 i think
Step-by-step explanation:
Answer:
The answer is -69,420 ! 69,420 - 69,420 = 0. next you multiply it and its 0 again then you add it 69,420 then subtract it equals 0 then subtract again it equals -69,420 then multiply it equals -69,420 then you have to add 69,420 it equals 0 again then you subtracted 69,420 and that means its -69,420!
Step-by-step explanation:
Which is the graph of g(x) = (0.5)x+ 3 – 4?
1
Answers
Answer:
It will look like this
Step-by-step
I got stuck on a question on edge can anyone help?
Answers
Answer:
A and D
Step-by-step explanation:
12 is what
% of 200?
Answers
Answer: 6%
pls give me brainliest ty
Step-by-step explanation:
PLEASE HELP 15 POINTS HURRY!!!!!
Answers
Answer:
B. A. D.
Step-by-step explanation:
solve this please .......
Answers
Answer:
The sum of reciprocals is 2/3.
You don't need complex numbers to solve this, but if you try to find a and b you will need complex numbers.
Step-by-step explanation:
a+b = 2
a*b = 3
1/a + 1/b = x
(a*b)*(1/a + 1/b) = (a*b)x
b + a = (a*b)(x)
2 = 3x
x = 2/3
b = 2 - a
a*(2 - a) = 3
-a^2 + 2a = 3
-a^2 + 2a - 3 = 0
a^2 - 2a + 3 = 0
let's solve the quadratic equation
a^2 - 2a + 3 = a^2 - 2a + 1 + 2 = (a - 1)^2 + 2 = 0
(a - 1)^2 = -2
[tex]a_1 - 1 = \sqrt{2}i\\a_1 = 1+\sqrt{2}i\\\\a_2 - 1 = -\sqrt{2}i\\a_2 = 1 - \sqrt{2}i\\[/tex]
these options correspond to a and b from the original question.
Write an equation that can be used to answer the question. Then solve. Round to
the nearest tenth if necessary.
How high is the ramp?
21 ft
19 ft
Oa h + 192 = 212: 8.9 ft
Ob. 21° - 192 = 12:28.3 ft
Och + 192 = 212; 80 ft
Od. h + 19 = 21; 2 ft
what’s the answer
Answers
Giving Brainliest if answer is correct
if x varies directly as y and x=3 when y=15 find the value of x when y=25
Answers
Answer:
Step-by-step explanation:
x=5
Answer:
x is 5.
Step-by-step explanation:
X varies directly with y, so we can use the equation x = yk (with k standing for the constant of variation) to find what the constant is. Substitute 3 for x and 15 for y
3 = 15k
Now divide both sides by 15.
3/15 = k
3/15 simplifies to 1/5.
1/5 = k
Now that we know the constant, then what we need to do is find 1/5 of 25 to get x.
1/5(25) = x
Multiply 1/5 by 25 to get 5.
5 = x
The problem is solved.
X will be 5 in this scenario.
Please help me with this
Answers
Answer:
Its B
Step-by-step explanation:
How do you write 1/9 as a decimal?
Answers
Answer:
0.111111111
Step-by-step explanation:
Answer:
0.11
Step-by-step explanation:
The ones are never-ending so if you round it, it is 0.11