Write an exponential decay function to model each situation. Compare the average rates of change over the given intervals.
21. Initial value: 50
Decay factor: 0.9
1 ≤ x ≤ 4 and
5 ≤ x ≤ 8
Answers
The model of the exponential functions is written as
21:
f(x) = 50(0.9)ˣ
average rate of change
1 ≤ x ≤ 4 is -45 ≤ x ≤ 8 is -2.722:
f(x) = 25(0.8)ˣ
average rate of change
2 ≤ x ≤ 4 is -2.96 ≤ x ≤ 8 is -1.2How to write the exponential function to model the dataConsidering the given problem, f(x) = a(b)^x
the initial value = a
the base = b
the exponents = x
21.
Initial value: 50
Decay factor: 0.9
1 ≤ x ≤ 4 and
5 ≤ x ≤ 8
x = 1
f(x) = 50(0.9)^1
f(x) = 45
x = 4
f(x) = 50(0.9)^1
f(x) = 32.805
average rate of change for x = 1 and x = 4
average rate of change = (32.805 - 45) / (4 - 1)
average rate of change = -4.065
average rate of change for x = 5 and x = 8
average rate of change = (50(0.9)^5 - 50(0.9)^8) / (5 - 8)
average rate of change = 8.0011 / -3
average rate of change = -2.667
22.
Initial value: 25
Decay factor: 0.8
2 ≤ x ≤ 4 and
6 ≤ x ≤ 8
f(x) = 25(0.8)^x
average rate of change for x = 2 and x = 4
average rate of change = (25(0.8)^2 - 25(0.8)^4) / (2 - 4)
average rate of change = 5.76 / -2
average rate of change = -2.88
average rate of change for x = 6 and x = 8
average rate of change = (25(0.8)^6 - 25(0.8)^8) / (6 - 8)
average rate of change = 2.3593 / -2
average rate of change = -1.1797
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Related Questions
Sweet Branch Grocery sells 5 bottles of soda for $6. As of next week, though, the price per bottle will increase by 10%. How much will 12 bottles of soda cost next week?
Answers
Answer:
15.84
Step-by-step explanation:
6 divided by 5 is 1.2
1.2 increased by 10% is 1.32
1.32 x 12 is 15.84
(NOT SURE IF IM RIGHT)
Dan is cutting 4.75-foot lengths of twine from a 249-foot spool of twine. He needs to cut 42 lengths and says that 40.5 feet of twine will remain. Show that this is reasonable.
Answers
To show that Dan's statement is reasonable, we can set up an equation to represent the situation. Let's let x represent the number of feet of twine that Dan has cut.
We can then set up the following equation: [tex]4.75x = 249 - 40.5[/tex]
Solving for x, we find that x = 42. This means that Dan has cut 42 lengths of twine, which is what he said he would do.
Since the number of lengths of twine that Dan has cut and the amount of twine that will remain match what Dan said, his statement is reasonable.
The price of milk increased from $3.25 to $3.75. What is the percent of change for the price of milk to the nearest tenth?
Answers
Answer:
15 % increase
Step-by-step explanation:
2(m + 2) =22 Describe what it means to distribute the 2 to each term inside the parenthesis
Answers
Answer:
Step-by-step explanation:[tex]\frac{2(m+2)}{2}[/tex]
step 1
2(m+2)=22=2x11
step 2
:[tex]\frac{2(m+2)}{2}=\frac{2*11}{2}[/tex]
step 3
(m+2)=11
step 4
m=11-2=9
Answer: (see below)
Step-by-step explanation:
2 distributed to each term inside 2(m + 2) looks like this:
2m + 4
first multiply 2xm, then 2x2
Now you have an expression where you can solve for m:
2m + 4 = 22
2m = 22 - 4 = 18
m = 18/2 = 9
13 friends go to a restaurant. The bill comes to $170. The restaurant's policy is to add on a tip that is 18% of the bill for parties of 8 or more. What is the total cost, with the tip?
Answers
Question. {Please explain your answer}
(Which statement correctly describe the data shown in the scatter plot?)
A. The scatter plot shows no association.
B. The scatter plot shows a linear association.
C. The point (2, 14) is an outlier.
D. The scatter plot shows a negative association.
Answers
Answer:
The scatter plot shows a (positive) Liner association.
Step-by-step explanation:
just by looking at the graph, you can see a positive correlation for each point, because they line up to form an almost straight line upward. I hope this helped!
What is the coefficient in the expression 5 − 6?
Group of answer choices
6
5x-6
5
5x
Thank u!
Answers
Answer:
9
hope you like it
Answer:
5
Step-by-step explanation:
coefficient is the number before the variable (x)
Solve the following inequality. 4x-1> -9
A X<-5/2
B X<-2
C X>-5/2
D X>-2
Answers
Answer:
ANS:- D) x > -2
Step-by-step explanation:
4x -1 > -9
4x > -9 +1
4x > -8
x > -8/4
x > -2
Describe a math tool you could use to determine if a relation is a function. Explain how you would use it. Select all that apply.
Multiple select question
A)
I could use a mapping diagram. If more than one arrow points from an input value to the output values, I know it is not a function.
B)
I could use a straight object like a pencil. If the pencil intersects a graph at more than one point when it is held vertically, I know it is not a function.
C)
I could use a table. If I see that there is more than one output for an input, then the relation is a function.
D)
I could use a straight object like a pencil. If the pencil intersects a graph at more than one point when it is held horizontally, I know it is not a function.
E)
I could use a mapping diagram. If more than one arrow points from an output value to the input values, I know it is not a function.
Answers
Answer:
C, Identify the input values. Identify the output values. If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.
C
I'm posting this question again because I seriously need help with it and it's only 8th grade math
Answers
Answer:
Step-by-step explanation:
Remember to put >= or <= for solid lines and < and > for dashed
1. =y >= 1/3x -4
2. y < 2x
3. y>= 3
4. y<= -3/2x +4
Answer: add some description not just the picture also I think you just have to count them like the (-) and the (+) with the numbers on the side
Step-by-step explanation:
The data below shows the ratio of brown to green crayons in four kindergarten classrooms. 13 to 19 15 to 28 18 to 32 30 to 68 Which table below correctly shows these ratios in a three-column table?
Answers
Answer:
Brown 13 15 18 30
Green 19 28 32 68
Total 32 43 50 98
Step-by-step explanation:
(ik this is rly late im just doing it for a quest lol)
Evaluate the expression:
4 x (10+8) + 3 to the power of 2
Thank u!
Answers
Answer:
Step-by-step explanation:
81
Step-by-Step:
4x(10+8)+3^2
4x(10+8)+9
4x(18)+9
72+9
81
Help. I'll mark as brainlist.
Answers
Answer:
SUT and TUS
Step-by-step explanation:
Answer: Angle U, Angle SUT
Step-by-step explanation:
Angle U- the point of the angle
Angle STU- the points of the angle
Solve each word problem. Show your work and include the correct units.
1. Each side of a square barn is 9 meters long.
a. What is the barn’s perimeter? ___________________
b. What is the barn’s area? ___________________
2. A rectangular piece of metal is 10 inches wide and 14 inches long.
a. What is the perimeter? ___________________
b. What is the area? ___________________
3. A rectangular cornfield has a length of 7 kilometres and an area of 63 square
kilometres.
a. What is the width of the cornfield? ___________________
b. What will be the area if the length and width are doubled? ______________
4. Eric has 54 yards of fencing to use for a flowerbed. Some possible measurements are
shown below. For which flowerbeds does Eric have enough fencing? Color in all the
possible answers.
A.
length = 30 yards
area = 300 square yards
B.
length = 20 yards
width = 5 yards
C.
width = 12 yards
perimeter = 48 yards
D.
length = 26 yards
width = 22 yards
E.
length = 16 yards
width = 14 yards
F.
width = 9 yards
area = 162 square yard
Answers
Answer:
Step-by-step explanation:
1
perimeter = 9 · 4 = 36 m
area = 9² = 81 m²
2
perimeter = (10+14) · 2 = 24 · 2 = 48 in
area = 10 · 14 = 140 in²
3
width = 63 : 7 = 9 km
9 · 2 = 18 km
7 · 2 = 14 km
area = 18 · 14 = 252 km²
4
A 300 : 30 = 10
(10 + 30) · 2 = 40 · 2 = 80 (no)
B
(20 + 5) ·2 = 25 · 2 = 50 yd (ok)
C
perimeter is 48 yd (ok)
D
(22 +26) · 2 = 48 · 2 = 96 yd (no)
E
(16 + 14) · 2 = 30 · 2 = 60 yd (no)
F
length = 162 : 9 = 18 yd
(18 +9) · 2 = 27 · 2 = 54 yd (ok)
Answer:
1
perimeter = 9 · 4 = 36 m
area = 9² = 81 m²
2
perimeter = (10+14) · 2 = 24 · 2 = 48 in
area = 10 · 14 = 140 in²
3
width = 63 : 7 = 9 km
9 · 2 = 18 km
7 · 2 = 14 km
area = 18 · 14 = 252 km²
4
A 300 : 30 = 10
(10 + 30) · 2 = 40 · 2 = 80 (no)
B
(20 + 5) ·2 = 25 · 2 = 50 yd (ok)
C
perimeter is 48 yd (ok)
D
(22 +26) · 2 = 48 · 2 = 96 yd (no)
E
(16 + 14) · 2 = 30 · 2 = 60 yd (no)
F
length = 162 : 9 = 18 yd
(18 +9) · 2 = 27 · 2 = 54 yd (ok)
Step-by-step explanation:
Carmela mixes 3/4 kilograms of walnuts, 1/2 kilograms of almonds,and 1/4 kilograms of pecans together. She divides the mixed nuts into 3/10 kilogram bags. How many bags of mixed nuts does she have. PLEASE HELP DUE TOMORROW.
Answers
Answer:
5 bags of mixed nuts.
Step-by-step explanation:
First, we add the amount of nuts together.
3/4 + 1/4 = 1
1 + 1/2 = 1 1/2
1 1/2 = 3/2 as an improper fraction.
Then we divide 3/2 by 3/10
To divide fractions, use "Keep, Switch, Flip"
Keep the first number, switch the sign, and flip the second fraction.
3/2 * 10/3 = 30/6 = 5.
Can someone help, please
Answers
The standard equation is y=mx+b. The "m" in the equation symbolizes the slope. The question's equation is [tex]y=\frac{2}{9} +2[/tex].
[tex]y=mx+b\\y=\frac{2}{9} +2[/tex]
Which value matches the "m"? [tex]\frac{2}{9}[/tex]
Thus, the slope in this equation is [tex]\frac{2}{9}[/tex]
Hope this helped :)
Can someone help, please
Answers
Answer:9/4, simplified it is 2 and 1/4, or 2.25
Step-by-step explanation: y value moves up from 1 to 10, x value moves right from 6 to 10.
Answer: 9/4
work:
1-10=-9
6-10=-4
do this one [tex]x +4+9999999999[/tex]
Answers
Answer:
10000000003x
Step-by-step explanation:
x+4+9999999999
Solution
Given,
or, x+10000000003
Therefore,
Ans=10000000003x
Simplified answer:
x + 100000000003
Step-by-step explanation:
x + 4 + 99999999999 = x + 100000000003
Mr. F's bathtub drains at a rate of 2 gallons per minute but fills at 3.5 gallons per minute. After a 4000-calorie dinner, Mr. F forgot to close the drain before filling his 60 gallon tub. How long did it take for the tub to fill? Express your answer in minutes.
Answers
40 minutes
Step-by-step explanation:
It will take 40 minutes because if the water drains at a rate of 2 gallons a minute but fills at 3.5 gallons a minute, that will mean that the water will still fill at 1.5 gallons per minute.
If you multiply 1.5 gallons by 20 minutes the tub will be half full with 30 gallons of water so that means if you multiply 20 minutes by 2 it will mean that the tub will have 60 gallons of water and it would have taken 40 minutes to fill.
There are 15 sedans on a used car lot, along with 54 other vehicles.
What is the probability that a randomly selected vehicle will be a sedan?
Write your answer as a fraction or whole number.
Answers
Answer:
5/23
Step-by-step explanation:
54+15=69
15/69=5/23
The Probability of selecting a sedan is 22%.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The degree to which something is likely to happen is basically what probability means.
Given that there are 15 sedans and 54 other vehicles, the total number of vehicles on the lot is:
Total number of vehicles
= Number of sedans + Number of other vehicles
= 15 + 54
= 69
So, the Probability of selecting a sedan
= Number of sedans / Total number of vehicles
= 15 / 69
= 5/23
= 0.22
= 22%
Learn more about Probability here:
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im tired of typing. sorry mb, the question is in the first picture though!!1 asnwers in the other pic
Answers
the slope of the graph is 1/3 (rise 1, run 3) and the y intercept is at 0 so the equation of the line is y=1/3 x
if we plug in the x values to the equation, we will get the corresponding y values in the table:
y=1/3(12)=4
y=1/3(15)=5
y=1/3(18)=6
y=1/3(21)=7
While Zihao was pooping, Zihao-2 ringed to the door. Find the speed of Zihao to open the door, when toilet is on 25 m in front of the door for 5 sec
Answers
Answer:
Until you wipe
Step-by-step explanation:
Why would you open the door if your still on the toilet and haven't wiped?
this alien line stuff is confusing me like wth.
Answers
im pretty sure that your answer is right. the slope is 4
Answer: you are right
Evaluate this expression when c = -2 and d = 2:
(c^2+d^2) -2 (c^2-d^2)
A. 0 B. 8 C. -8 D. 16
Answers
Answer: B i hope this helped :)
Step-by-step explanation:
Explanation:
Hope this helps<33!
y - 1/6 + 5/18
A | 1/9
B | 1/4
C | 4/9
D | 1 2/3
Answers
y + [tex]\frac{1}{9}[/tex]
Step-by-step explanation:Here are the steps to your problem:1. Add the numbers
y - [tex]\frac{1}{6}[/tex] + [tex]\frac{5}{18}[/tex]
y + [tex]\frac{1}{9}[/tex]
Solution:y + [tex]\frac{1}{9}[/tex]
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Will you need to change the inequality sign in the problem 5x+2+5x<16? Explain your answer. 20 Points
Answers
Answer:
no
Step-by-step explanation:
10x+2 < 16
10x < 14
x <14/10
Do not change sign because you are not dividing by a negative number
Under standard atmospheric conditions, water will not remain a liquid if its temperature is less than or equal to 0°C or if it is greater than or equal to 100°C. Suppose you have a cup of water that is room temperature, or 20°C.
a. Write a compound inequality to represent the number of degrees of Celsius c that the temperature of the cup must change to longer be liquid.
Answers
Ur mom
Anyways it would be 74 cilces and 4 farnheight
Hello. This is a very quick question, that requires little effort. I am currently working on my math assignment, and for the project I have to measure five different people. Unfortunately, I don't have enough people to measure. You will get 100 points just for answering this :) But if you do a troll answer, I'll report you :)
"Using a tape measure or ruler, measure the length (in inches) of a person’s left foot and then measure the length (in inches) of that same person’s forearm (between their wrist and elbow). Refer to the diagrams below. You will have two measurements for each person."
Answers
My foot is 17 inches and my forearm is 43 inches
Can someone help, please
Answers
The answer to this is
(0, -13/10)
__________________________________________________________
To find the y-intercept, substitute in 0 for x and solve for y.
(Like my profile picture)
Which of the following sequences represents an arithmetic sequence?
A -5, -3, -1, 1, ...
B -7, -4, 1, 4, ...
C 1, 4, 9, 16, ...
D 2, -4, 8, -16, ...
Answers
Answer:
Step-by-step explanation:
Question
Which of the following sequences represents an arithmetic sequence?
A -5, -3, -1, 1, ...
B -7, -4, 1, 4, ...
C 1, 4, 9, 16, ...
D 2, -4, 8, -16, ...
-5, -3, -1, 1