Answers
Given:
The table of values of an exponential function.
To find:
The missing values in the exponential function.
Solution:
The general exponential function is defined as:
[tex]y=a(b)^x[/tex] ...(i)
Where, a is the initial value and b is the growth factor.
First point from the given table is (1,10). It means, the equation (i) must be true for (1,10).
[tex]10=a(b)^1[/tex] ...(ii)
Second point from the given table is (2,20). It means, the equation (i) must be true for (2,20).
[tex]20=a(b)^2[/tex] ...(iii)
Dividing (iii) by (ii), we get
[tex]\dfrac{20}{10}=\dfrac{a(b)^2}{ab}[/tex]
[tex]2=b[/tex]
Putting [tex]b=2[/tex] in (ii), we get
[tex]10=a(2)^1[/tex]
[tex]\dfrac{10}{2}=a[/tex]
[tex]5=a[/tex]
Putting [tex]a=5,b=2[/tex] in (i), we get
[tex]y=5(2)^x[/tex]
The required exponential function for the given table of values is [tex]y=5(2)^x[/tex]. So, the missing values are 2 and x, where 2 is in the base and x is in the power.
Related Questions
If Mike loses $5 per week, how much does he lose in 4 weeks?
Answers
Answer:
$ 20Step-by-step explanation:
[tex]1week \: = 5 \\ 4 \: weeks = x \\ \\ x = 20[/tex]
hope this helps you.
Can I have the brainliest please?
Have a nice day!
Pam and her grandma are planning to make a quilt together. The quilt will be made out of fabric squares that measure 6 inches on each side. The quilt will have 3 more squares along its longer edge than it will have along its shorter edge.
If there are x fabric squares along the quilt's shorter edge, find an expression for f(x), the length of the quilt's shorter edge in inches.
f(x)=
6x
Next, find an expression for g(x), the length of the quilt's longer edge in inches.
g(x)=
Which function can you use to find the area of the quilt in square inches?
Answers
Answer:
There are x squares on the shorter side, each square measures 6 inches.
The length of the shorter side is:
f(x) = x*6 = 6xThe length of the longer side is:
g(x) = (x + 3)*6 = 6x + 18The area of the quilt is:
A = 6x(6x + 18) = 36x² + 108xThere are 4 roses for every 7 carnations in a bouqeuet. Mr rodriguez buys a bouqeuet with 12 roses in it. How many total flowers are in the bouqeuet Mr rodriguez bought?
Please explain step by step I dont get it.
Answers
Answer:
33 total flowers are in the bouquet Mr Rodriguez bough
Step-by-step explanation:
So for every 4 roses there are 7 carnations meaning the ratio is 4:7
4 times x = 12
x=3
So we do the same for carnations
7 x 3 = 21
Now we add to find the total
21+12=33
33 total flowers
What is the theoretical probability that the spinner below will land on 6 if someone spins it 48 times?
Answers
Answer:
1/4 or 12*
Step-by-step explanation:
There are 8 possibilities. 2 of them are 6.
2/8=1/4
1/4 of 48 is 12
*The theoretical probability doesn’t change no matter how many times you spin the spinner. It will always be 1/4. (Or 0.25, or 25%). That could be what they’re asking. If you spun it 48 times, it would probably land on a six 12 times. That could also be what they’re asking for. 12:48 = 1:4.
Can someone give me a fake band name???
Answers
Answer:
loaded diper
Step-by-step explanation:
-A sequence is a list of numbers or obje
What is a pattern?
-A pattern is a repetitive sequence and
numbers and almost everywhere you ca
What's More
A. Directions: Give the pattern rule of t
Rul
1. 1, 4, 7, 10, 13
2.2, 8, 32, 128, 512
Rul
Answers
Answer:
1. Add 3
2. Multiply 4
Step-by-step explanation:
Given
[tex](1)\ 1, 4, 7, 10, 13[/tex]
[tex](2)\ 2, 8, 32, 128, 512[/tex]
Required
The rule
[tex](1)\ 1, 4, 7, 10, 13[/tex]
This is a linear function because successive terms have a common difference
The common difference between each term is:
[tex]d = 4 - 1 = 3[/tex]
[tex]d = 7 - 4 = 3[/tex]
[tex]d = 10 - 7 = 3[/tex]
[tex]d = 13 - 10 = 3[/tex]
The above shows that 3 is [tex]added\ to\ each\ term[/tex] to get the next term.
Hence, the rule is: Add 3
[tex](2)\ 2, 8, 32, 128, 512[/tex]
This is a geometric function because successive terms have a common ratio
The common ratio between each term is:
[tex]r = 8/2 = 4[/tex]
[tex]r = 32/8 = 4[/tex]
[tex]r = 128/32 = 4[/tex]
[tex]r = 512/128 = 4[/tex]
The above shows that 4 [tex]is\ multiplied\ to\ each\ term[/tex] to get the next term.
Hence, the rule is: Multiply 4
what is the area of the shaded region? use 3.14 for pi
Answers
Answer:
13.8
Step-by-step explanation:
Area of square = πr²
=22/7 × 4²
=50.2
Area of square = l²
=8²
= 64
Area of shape is 64 - 50.2 = 13.8
Answer:
The answer is 13.8
Step-by-step explanation:
Yes
50 pts please help asap (:
Answers
Answer:
d. 8 units
Step-by-step explanation:
If AC = 16 units then the length of CB is 8 units because DB is perpendicular bisector from the centre of circle.
Answer: B
Step-by-step explanation: I took the quiz
Hope this helps
how to solve by factoring
x^2 + x = 0
Answers
Answer:
x=0 and x=-1
Step-by-step explanation:
Given: x^2+x=0
Factor: x(x+1)=0
Use Zero Product Property: x=0 and x+1=0
Therefore, x=0 and x=-1
what is the shape identify in the image
Answers
Answer:
it is a triangular prism
Which number has the least absolute value?
Answers
Explanation: The bigger the negative number, the lower the number actually is.
7n - 4 (8n+4) = 159
Answers
Answer:
n = -7
Step-by-step explanation:
Use distributive property:
7n - 32n - 16 = 159
Combine like terms
-25n - 16 = 159
Add 16 to both sides to isolate variable n
-25n = 175
Divide both sides by -25 to isolate variable n
n = -7
Check your work:
7(-7) - 32(-7) - 16 = 159
-49 + 224 - 16 = 159
159 = 159
please help meeeee i will give brainlyest
Answers
Answer:
answer is 63 min
Step-by-step explanation:
math+calculator like and subscribe to yourmom.com31
The side lengths of a rectangle are all multiplied by 5. What happens to its perimeter?
Answers
Answer:
The perimeter is multiplied by 5.
Step-by-step explanation:
Perimeter of a rectangle:
The perimeter of a rectangle with sides l and w is given by:
[tex]P = 2(l + w)[/tex]
The side lengths of a rectangle are all multiplied by 5.
This means that [tex]l = 5l, w = 5w[/tex]. So
[tex]P_M = 2(5l + 5w) = 2*5(l+w) = 10(l + w)[/tex]
What happens to its perimeter?
The rate is:
[tex]\frac{P_M}{P} = \frac{10(l+w)}{2(l+w)} = 5[/tex]
The perimeter is multiplied by 5.
If x=3 and y=7, evaluate the following expression: 100 − 3 ( 3 − 4x )
Answers
Answer:
[tex]100 - 3(3 - 4x) \\ = 100 - 3(3 - 4 \times 3) \\ = 100 -27 \\ = 73[/tex]
Answer:
873
Step-by-step explanation:
100 - 3 ( 3- 4x ) 97 ( 3 - 4×3 )97 (3 - 12 ) 97 × 9 873A bicycle is originally priced at $60. The online retailer gives a discount and the bicycle is now priced at $42. Enter the percentage discount for the cost of the bicycle.
Answers
Answer:
30% ywww
Step-by-step explanation:
what is the area of a right triangle with sides 7ft 24ft and 25ft?
Answers
Answer:
84 ft^2
Step-by-step explanation:
[tex] \frac{7 + 24 + 25}{2} = 28[/tex]
The area is:
[tex] \sqrt{28 \times (28 - 7) \times (28 - 24) \times (28 - 25)} [/tex]
[tex] = 84 \: {ft}^{2} [/tex]
brainiest exchange give me and I will give you 2+2
Answers
Answer:
4
Step-by-step explanation:
and sure
Answer:
4
Step-by-step explanation:
Kristin charges $30 to train a small dog, and $50 to train a big dog. If Kristin trains 15 small dogs and 6 big dogs, how much money will she make?
Answers
Answer:
$750
Step-by-step explanation:
We can set up the equation 30x + 50y = z where x = the amount of small dogs, y = the amount of big dogs, and z = the total.
After plugging in the x and y values to solve for z, we are left with the following equation:
30(15) + 50(6) = 750
sin(30°)cos(45°) + cos(30°)sin(45°)
Answers
Step-by-step explanation:
sin(30°)cos(45°) + cos(30°)sin(45°)=1+√3/2√2
cos45 = √2/2
cos30 = √3/2
sin45 = √2/2
answer: √2 + √6
—————
4
SAT scores: The College Board reports that in 2009, the mean score on the math SAT was 582 and the population standard deviation was =σ120. A random sample of 20 students who took the test in 2010 had a mean score of 515. Following is a dotplot of the 20 scores. (a) Are the assumptions for a hypothesis test satisfied? Explain. (b) If appropriate, perform a hypothesis test to investigate whether the mean score in 2010 differs from the mean score in 2009. Assume the population standard deviation is =σ120. What can you conclude? Use the =α0.10 level of significance and the critical value method.
Answers
Answer:
we can conclude that there is no significant evidence to conclude that the mean score in 2010 differs from the mean score in 2009.
Step-by-step explanation:
H0 : μ = 582
H1 : μ < 582
Test statistic :
T = (xbar - μ) ÷ σ/√n
Xbar = 515 ; n = 20 ; σ = 120
T = (515 - 582) ÷ 120/√20
T = -67 / 26.832815
T = 2.50
Pvalue at t score = 2.50 ; df = 19 is 0.0187
At α = 0.0187
Pvalue > α ; Hence, we fail to reject the Null
Hence, we can conclude that there is no significant evidence to conclude that the mean score in 2010 differs from the mean score in 2009.
A LOT OF POINTS!!
Suppose you borrow $40,000 at 13% APR for a 12-year term to be paid monthly. Your monthly payment is $450.00.
How much of your first payment goes toward interest?
Make sure you show your work to earn full credit.
Answers
Answer:
You get $45,200 first with interest with the 5400 you made in 1 year that dedeucts
Step-by-step explanation:
find the gradient of the line
with the equation 3x+4y=10
Answers
PLEASE GIVE ME AN ANSWER!!!!ILL MARK BRAINLIEST ANSWER
Answers
Answer:
3 3/4
Step-by-step explanation:
3.75 square ft per hr.
5/8 x 6 = 3.75
I got this question
8% of $796.25 is how much?
Answers
8/100*796.25
=63.7%
Answer:63.7%
Answer: Hello, there! your Answer is below
63.7 would Be the correct answer
Step-by-step explanation: Below Is Info About How to Calculate Precentage UwU
how to calculate percentage of a number. Use the percentage formula: P% * X = Y
Convert the problem to an equation using the percentage formula: P% * X = Y.
P is 10%, X is 150, so the equation is 10% * 150 = Y.
Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.
Tinisha is planning a birthday party. She can buy:
10 balloons, 8 cupcakes, and 8 hats for $50
5 balloons, 9 cupcakes, and 7 hats for $46, or
12 balloons, 7 cupcakes, and 9 hats for $51
Using b for the number of balloons, c for the number of cupcakes, and h for
the number of hats, write a system of equations to represent this situation.
Answers
Answer:
b+c+h=50
Step-by-step explanation:
Its the first one because you need to have the same amount of hats as cupcakes cause the hat really stands for people.
Do 5 yd 12 yd 13 yd make a right angle?
Answers
Calculate the mass of NaOH in 0.2 moles of NaOH
Answers
Answer:
0.2M i.e
Step-by-step explanation:
In sixteen years Paul will be 48 years old.
How old is he now?
Answers
Answer:
32 years old
Step-by-step explanation:
48-16=32
Answer:
Paul is 32 years old
Step-by-step explanation:
48 - 16 = 32
I need so much help help me please UwU
Answers
Answer:
Line A: y = 3x + 3
Line B: y = -1/3x + 3
Step-by-step explanation:
Line A points: (0, 3) and (1, 6)
Slope:
m=(y2-y1)/(x2-x1)
m=(6-3)/(1-0)
m= 3
y - y1 = m(x - x1)
y - 3 = 3(x - 0)
y - 3 = 3x
y = 3x + 3
Line B points: (0, 3) and (9, 0)
Slope:
m=(y2-y1)/(x2-x1)
m=(0-3)/(9-0)
m= -1/3
y - y1 = m(x - x1)
y - 3 = -1/3(x - 0)
y - 3 = -1/3x
y = -1/3x + 3