Write an exponential function to model the data in each table. Identify the growth or decay factor. (23) Picture
Answers
The model of the exponential functions show that
23: table 1 is a decay with a rate of 50%24. tables 2 is a growth with a rate of 10%How to write exponential function to model the data in each tableConsidering the given problem, f(x) = a(b)^x
the starting = a
the base = b
the exponents = x
23. Table 1
At x = 0
f(x) = a(b)^x
(b)^0 = 1
solving for a
4 = a * (b)^0
4 = a
At x = 1
f(x) = a(b)^x
(b)^1 = b
substituting known variables
2 = 4(b)^1
b = 2/4
b = 0.5
for decreasing rate, b = 1 - 0.5 = 0.5
rate, r = 50%
24. Table 2
At x = 0
f(x) = a(b)^x
(b)^0 = 1
solving for a
100 = a * (b)^0
100 = a
At x = 1
f(x) = a(b)^x
(b)^1 = b
substituting known variables
110 = 100(b)^1
b = 110/100
b = 1.10
for increasing rate, b = 1 + r = 1.10, r = 0.10
rate, r = 10%
The base is what determines exponential growth or decay
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Related Questions
Harold buys hot dogs and water bottles for a fundraiser. He can buy a pack of 8 hot dogs for $6, and a pack of 6 water bottles for $4. He buys 192 hot dogs and bottles of water together, and spends a total of $136.
How many packs of hot dogs and packs of water bottles does Harold buy?
A. 16 packs of hot dogs and 12 packs of water bottles
B. 12 packs of hot dogs and 16 packs of water bottles
C. 10 packs of hot dogs and 15 packs of water bottles
D. 14 packs of hot dogs and 12 packs of water bottles
Answers
It’s the only answer that correctly adds up to 192.
Answer:
B
Step-by-step explanation:
hotdogs:
12 packs x 8 = 96
water:
16 packs x 6 = 96
total:
96 + 96 = 192
Model each pair of situations with exponential functions f and g. Find the approximate value of x that makes f(x) = g(x).
25. F: initial value of 100 decreasing at a rate of 5%
G: initial value of 20 increasing at a rate of 5%
Answers
The model of the exponential functions
25:
f(x) = 100(0.95)ˣg(x) = 20(1.05)ˣf(x) = g(x) at x = -46.5326
f(x) = 40(1.25)ˣg(x) = 10,000(0.84)ˣf(x) = g(x) at x = 113.11How to model each pair of the functions with exponential functionConsidering the given problem, f(x) = a(b)^x
the starting = a
the base = b
the exponents = x
25.
F: initial value of 100 decreasing at a rate of 5%
a = 100, rate, r = 5%, b = 1 - 0.05 = 0.95
f(x) = 100(0.95)ˣ
G: initial value of 20 increasing at a rate of 5%
a = 20, rate, r = 5%, b = 1 + 0.05 = 1.05
g(x) = 20(1.05)ˣ
solving for f(x) = g(x)
20(1.05)ˣ = 100(0.92)ˣ
divide through by 20
(1.05)ˣ = 5(0.92)ˣ
x㏒(1.05) = ㏒(5 + (0.92)ˣ)
x㏒(1.05) = ㏒5 - x㏒0.92
x㏒(1.05) + x㏒0.92 = ㏒5
-0.015x = ㏒5
x = -46.53
26.
f: initial value of 40 increasing at a rate of 25%
a = 40, r = 25%, b = 1 + 0.25 = 1.25
f(x) = 40(1.25)ˣ
g: initial value of 10,000 decreasing at a rate of 16%
a = 10,000, r = 16%, b = 1 - 0.16 = 0.84
g(x) = 10,000(0.84)ˣ
solving for f(x) = g(x)
40(1.25)ˣ = 10,000(0.84)ˣ
divide through by 40
(1.25)ˣ = 250(0.84)ˣ
x㏒(1.25) = ㏒(250 + (0.84)ˣ)
x㏒(1.25) = ㏒250 - x㏒0.84
x㏒(1.25) + x㏒0.84 = ㏒250
0.0212x = ㏒250
x = 113.11
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What is the perimeter of a rectangle with a length of Eight and one-sixth feet and a width of Six and two-thirds feet?
Fourteen and three-ninths feet
Sixteen and two-sixths feet
Twenty-nine and four-sixths feet
Forty-eight and three-eighteenths feet
Answers
Answer:
Fourteen and three ninthn feet
Step-by-step explanation:
Just add them together and you get the answer.
Answer: Twenty-Nine and Four-Sixths feet
Step-by-step explanation:
Perimeter is the sum of all sides.
So we just add 8 1/6 + 8 1/6 + 6 2/3 + 6 2/3
but before we can add them up we need to make our fractions have the same denominators
so we multiply the 2/3 by 2 to give us 4/6 then we can add the fractions together
1/6 + 1/6 + 4/6 + 4/6 = 10/6 or 1 4/6
then add 8 + 8 + 6 + 6 + 1 4/6 = 29 4/6 feet
3.
(04.05 LC)
Which of the following inequalities matches the graph? (1 point)
graph of an inequality with a solid vertical line through the point 5, 0 and shading to the left of the line
x ≤ 5
x ≥ 5
y ≤ 5
y ≥ 5
Answers
Answer: The inequality that matches the graph is x ≤ 5. This is because the graph has a solid vertical line at x = 5 and the shading is to the left of the line. This indicates that all values of x that are less than or equal to 5 satisfy the inequality.
The inequality x ≥ 5 would not match the graph because the shading would be to the right of the line. The inequalities y ≤ 5 and y ≥ 5 do not match the graph because they are not in the correct form. Inequalities involving y have a graph with a horizontal line, not a vertical line.
(-1/3)⁴(-1/3)²
help please
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Can somebody help me with this question please. The question is in the attachment.
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Can someone help, please
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Answer:
Y=8x+9
Step-by-step explanation:
I hope this helped you
Charles is in charge of cooking broccoli and zucchini for a large group. He has to spend all $20.10 he has and can carry 11 pounds of veggies. Zucchini costs $1.60 per pound and broccoli costs $2.10 per pound. How many pounds each of zucchini and broccoli can Charles get so that he spends all $20.10 and gets 11 pounds of veggies? Let x represent the number of pounds of zucchini and y represent the number of pounds of broccoli. Show ALL work!
Answers
Answer:
Total equation: X + Y = 11 pounds
Cost equation: 1.60X + 2.10Y = 20.10
Number of Pounds of Zucchini = 6
Number of Pounds of Broccoli = 5
Step-by-step explanation:
You get the equations by just pulling the information from the text.
We then take the total equation and rearrange it to solve for one of our values. I will be using X
X + Y = 11 so first subtract X from both sides to get
Y = 11 - X so now we know what Y equals
next take the cost equation and input X in wherever it shows up so
1.60 (X) + 2.10 (11 - X) = 20.10
now distribute 2.10 to the values in the parathesis to get
1.60X + 23.1 - 2.10X = 20.10
now combine like terms
-0.5X + 23.1 = 20.10
now subtract 23.1 from both sides
-0.5X = -3
now divide both sides by -0.5
X = 6
so now we know that he both 6 pounds of zucchini now plug that into the total equation
6 + Y = 11
subtract 6 from both sides
Y = 5
Write the inequality shown by the graph.
Answers
Answer: X<1 1/2
Step-by-step explanation:
A swimming pool is being drained at a rate of 50 gallons per hour. How many milliliters per second is this? Round to the nearest tenth.
Answers
Answer: 3154.16 milliliters / second
Step-by-step explanation:
1 gallon = 3.785 liters
1 liter = 1000 milliliters.
So multiply to convert: 1 gallon x 3.785 liters/gallon x 1000 milliters/liter = 3785 milliters ; 50 gallons = 50*3785 = 189250 milliliters
1 hr = 60 seconds 50 gallons per hour = 189250 mililiters/60 seconds =3154.16 milliliters/second
result : 50 gallons per hour = 3154.16 milliliters / second
please help?! ...i don't understand
Answers
Answer:
16.449 = 16.4
9.84 = 9.8
by estimating = 26.2
Answer:
16.5+9.8=26.3
Step-by-step explanation:
The equation is 16.449+9.84. We need to add these together after we round them to the nearest tenth. Well with decimals it goes ones, tenths, hundreths. So The second number past the decimal on the right side, is the one that we are rounding. If the number is greater than 5 then we move the number to the next tenth value.If its less than f5 we do the complete opposite.
16.449 is going to be rounded to be 16.5.
9.84 is going to be rounded to be 9.8
Now that our numbers are rounded we can add them.
16.5+9.8=26.3
I hope this helps!!!
Any additional help with rounding to the nearest tenth you could, if you want, use the website nearesttenth.com (Just to help you, I don't work with that website and not trying to advertise it like that).
What is the equation for the line in slope-intercept form?
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The table shows the length and width of proportional rectangles.
Length (in inches) | 6 | 9 | 18| 24 |
Width (in inches) | 10 | 15 | 30 | 40 |
Using the table, find the width of a rectangle that has a length of 42.
A) 45
B) 50
C) 60
D) 70
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Write the inequality shown by the graph.
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hope this helped :)
An international company has 23,700 employees in one country. If this represents 18.4% of the company's employees, how many employees does it have in total?
Answers
Answer:
128804.35 or 128804 because you cant have .35 of a person
Step-by-step explanation:
turn it into a fraction 18.4 over 100 and 23,700 over x. then cross multiply
Can someone help, please
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Answer: y = 10x - 10
This means 10 goes into each box, without any minus symbols.
==========================================
Reason:
Recall that slope-intercept form is y = mx+b
m = slopeb = y-interceptWe simply replace m with 10 since this the slope. We replace b with -10 because it's the y-intercept.
So,
y = mx+b
y = 10x+(-10)
y = 10x - 10
---------------
Extra info:
If you wanted to graph this, then I would start at the y intercept location of (0,-10). Then move up 10 units and to the right 1 unit to arrive at (1,0). Draw a straight line through these two points.
To find the x intercept, replace y with 0 and solve for x. The equation 0 = 10x-10 solves to x = 1.
Answer: y=10x-10
Step-by-step explanation:
10 being the point the slope crosses the y-axis
-10 being the degree of the slope
In the diagram below, the numbers in each box is the sum of the two numbers below it.
Work out the missing numbers for boxes A, B and C.
Answers
Answer:
Step-by-step explanation:
mhm
A rectangular prism has a volume of 90 cubic feet. The prism has a height of 2 feet and a width of 3 feet. What is the length of the prism?
Answers
Answer: 15ft.
Step-by-step explanation: L= V divided by h times w = 90 divided by 3x2 = 15ft
what is the value of this expression
5 (9/12 - 1/4) + 0.5
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The answer to this is 3
__________________________________________________________
PEMDAS= Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction
__________________________________________________________
9/12 - 1/4 = 0.5
0.5 x 5 = 2.5
2.5 + 0.5 =3
Find the missing number/s so that the equation has One solution.
__x + 3 = –4x + 17
Select all that apply
A: -4
B: 5
C: 2
D: 7
Answers
Answer:
Step-by-step explanation:
D) -10 = -28 + 17
ANS:- -10 = -10
Equivalent Ratios
x y
3 4
9 ?
18 24
What number is missing from the table of equivalent ratios?
Responses
A 1212
B 1010
C 1616
D 15
Answers
Answer:
C
Step-by-step explanation:
Took the test
Anyone can help, please use the image!
Answers
Answer:
1. 18
2. 12
3. 10%
4. 20%
Step-by-step explanation:
4. Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation. (-2, 3); y= 1/2 x-1)
A. y equals one-half x plus 1.
B. y equals negative two x minus 1.
C. y equals one-half x minus 1.
D. y equals negative one-half x minus 1.
Answers
Answer:
y=-2x-1
Step-by-step explanation:
PLS HELP!!!! The revenue for a local photographer for the month is $1200. His costs include a studio rental of $600, props costing $105, materials fees of $115, and a make-up artist who charges $130. What is his total profit for the month?
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Answer: $250 profit
Step-by-step explanation:
600+105+115+130 = 950
1200 - 950 = $250 total profit
1200-600-130-115-105
(3,-2);slope [tex]\frac{1}{2}[/tex]
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Can someone help, please
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Answer:
9/2
Step-by-step explanation:
slope = (10-1)/(10-8)
9/2
Answer:9/2, simplified is 4 and 1/2, or 4.5
Step-by-step explanation: y value moved up from 1 to 10, x value move right from 8 to 10.
A student earned the scores in the data set in one course. {78, 64, 74, 92, 67} What is the mean of the scores?
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Answer: The mean is 75
Step-by-step explanation:
- You add the scores in the data:
78+64+74+92+67 = 375
- Then divide by the number of scores in the data:
there are 5 scores in the data,
1) 78
2) 64
3) 74
4) 92
5) 67
- So:
375/5 = 75 <--- mean
To calculate mean or average from a data set, add all the data points together and then divide by the number of points you added together.
In this case,
78+64+74+92+67= 375/5= 75
<3
Please answer all of them and I will give brainlest
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2) m=2 b=10, y=2x+10, non, positive
3)m=44 b=48, y=44x+49, non, negative
I can't do the last one
help meeeeeeeeeeeeeeeee
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Answer:
3205
Step-by-step explanation:
3÷3=9
3÷2=6
3÷5=15
Answer:
Step-by-step explanation:
One mile is about 1.6 km. How many miles are in 10 km?
(Please show work)
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Answer:
6.25 or 6 1/4
Step-by-step explanation:
10 ÷ 1.6 = 6.25 or 6 1/4