which of the following situations could be modeled by an exponential function?
A. The water level of a tank decreases by 5 gallons every day.
B. The amount of money collected by a charity increases by $5,000 each year.
C. A tree was 10 feet tall when purchased and grows at a rate of 2 feet per year.
D. The number of people in a stadium is decreasing at a rate of 45% every 10 minutes.
Answer: Option D.
Step-by-step explanation:
An exponential function is something like:
f(x) = A*(r)^x
Where:
A = initial amount.
r = rate of growth
x = variable.
This type of function is used to describe situations like "you have A dollars, and it increases by 30% each week"
or:
"There is a population of A animals, and it doubles each year"
Let's analyze briefly all the given options and see which one is an exponential function.
A) The water level of a tank decreases by 5 gallons every day.
This is a linear relation, if W is the initial amount of water, and x is the number of days, then the water level of the tank after x days is:
y = W - 5 gal*x
B) The amount of money collected by a charity increases by $5,000 each year.
The amount collected increases $5000 each year.
Then if in year 1 they collected A.
in year 2 they collected A + $5000
in year 3 they collected A + 2*$5000
We already can see the pattern, this is a linear relation:
in year X they colected A + (X - 1)*$5000
C) A tree was 10 feet tall when purchased and grows at a rate of 2 feet per year.
if y is the height of the tree, and x is the number of years, this can be written as:
y = 10ft + x*2ft
Again, a linear relation.
D) The number of people in a stadium is decreasing at a rate of 45% every 10 minutes.
Let's define x as each "lapse" of 10 minutes that passes.
If N is the initial number of people in te stadium, then after 10 minutes the number of people is = N*(1 - 45%/100%) = N*(1 - 0.45) = N*0.55
After another 10 minutes, the population decreases again.
N*0.55*(1 - 45%/100%) = N*0.55*0.55 = N*0.55^2
We can see the pattern here, this can be written as
People(x) = N*(0.55)^x
This is an exponential function.
PLEASE HELP. I AM STUCK!!!
Answer:
Step-by-step explanation:
Midsegment means it's the middle, or half-way . It chops the sides into even parts. The line that's the midsegment is going to be parallel to the base and half the size of the base. In other words, double the midsegment and that's equal to the base. Then, just solve for x.
Given the following equation answer each question below.
Is the following a growth or decay?
What is the domain?
What is the range?
What is the y-intercept? (enter answer as a point)
What is the asymptote? (enter answer as an equation)
Answer:
f(x)=
Step-by-step explanation:
A gas tank on a car holds 16 gallons of gasoline and can travel 480 miles on a full tank. how many miles can the car travel per gallon?
Answer:
30 miles per gallon
Step-by-step explanation:
James has 21 cups of flour. He will pour the flour equally into 4 containers. How many cups of flour will be in each container?
Answer:
5.25 cups of flour
Step-by-step explanation:
4 containers - 21 cups of flour
1 container - 21 cups of flour ÷ 4 = 5.25 cups of flour
Answer: 5 1/4 cups of flour will be in each container
Step-by-step explanation:
21 ÷ 4= 5.25
5.25= 5 1/4
hope this helps i have no idea why i am typing in bold letters
A small town currently has a population of 15,000. Each year the population decreases by 2.25%. What will the population be in 8 years
Answer: 12,503 people
Step-by-step explanation:
This is an exponential decrease so to find the population in 8 years you have to use a future value formula:
= Amount * (1 + rate) ^ number of years
= 15,000 ( 1 + (-2.25%)) ⁸
= 15,000 * (1 - 2.25%)⁸
= 12,503.32
= 12,503 people
There were 845 students using Schoology in IRSD in 2017. In 2016 , there were 608 students using Schoology in the district.
51.5% of all users access Schoology on mobile devices. How many users used mobile devices in 2016?
313.120 (round as you would like)
Step-by-step explanation:
First you take the 51.5%, and divide it by 100, you should get 0.515. Now multiply with the 608 students, your answer should be 313.20, Ta Da!!! its right!! P.S You should also round (to 313) Please make this brainliest
Answer:
THIS WEBSITE SUCKS MY
Step-by-step explanation:
F IT
The population of a school is 800 and is decreasing at a rate
of 2% per year; 4 years
Answer:
i think the answer is 738
Write the following expression using symbolic language.
1) Five less than the product of seven and a number x
2) The difference of nine times a number y and eighteen
3) Half a number n increased by four times the number
4) Twice the sum of a number w cubed and twenty-three
Answer:
1) 7x - 5 2) 9y - 18 3) 0.5n + 4n 4) 2(w³+23) Step-by-step explanation:1)
The product of seven and a number x: 7·x = 7x
Five less than the product of seven and a number x:
7x - 52)
nine times a number y: 9·y = 9y
The difference of nine times a number y and eighteen:
9y - 183)
half a number n: 0.5n
four times the number: 4·n = 4n
Half a number n increased by four times the number:
0.5n + 4n4)
a number w cubed: w³
the sum of a number w cubed and twenty-three: w³+23
Twice the sum of a number w cubed and twenty-three:
2(w³+23)
PLEASE HELP THUS IS DUE IN AN HOUR
finding angle measures with trig. Find the missing angle measures. Round to the nearest whole number
Step-by-step explanation:
let angle be x
Step-by-step explanation:
relationship between perpendicular and hypotenuse is given by sin angle
sin x =p/h
sin x=13/26
x=sin-¹(13/26)=30°
2.relationship between perpendicular and base is given by tan angle
tan x =p/b
tan x =7/16
x=tan -¹(7/16)=23.63°
3.relationship between between perpendicular and base is given by tan angle
tan x =p/b
tanx=31/50
x=tan-¹(31/50)=31.8°
4.relationship between base and hypotenuse is given by cos angle
cos x =b/h
cos x=5/7
x=cos-1(5/7)=44.4°
5.relationship between perpendicular and hypotenuse is given by sin angle
sin x =p/h
sin x=4/14
x=sin-¹(4/14)=16.6
6..relationship between base and hypotenuse is given by cos angle
cos x=6/7
x=cos-¹(6/7)=31.0027
7.relationship between perpendicular and base is given by tan angle
.tanx=29/37
x=tan-¹(29/37)=38.09
8.relationship between perpendicular and hypotenuse is given by sin angle
.sin x=43/60
x=sin-¹(43/60)=45.78
9..relationship between base and hypotenuse is given by cos angle
cos x=32/44
x=cos-¹(32/44)=43.34
(x2+3x+2)+(3x2–x+1) Use algebra to find the sum
Answer: -2x²+2x+3
Step-by-step explanation:
Factoring -2x2+2x+3
The first term is, -2x2 its coefficient is -2 .
The middle term is, +2x its coefficient is 2 .
The last term, "the constant", is +3
Step-1 : Multiply the coefficient of the first term by the constant -2 • 3 = -6
Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is 2 .
-6 + 1 = -5
-3 + 2 = -1
-2 + 3 = 1
-1 + 6 = 5
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Please please help help me please please ASAP ASAP please ASAP thank you
Did this wrong sorry I thought it was greatest to least.
Answer:
-6, -1, 0, 4, 15
Step-by-step explanation:
the higher the negative number is, the smaller it is. its like being in debt
A photographer charges $200 to take photos of a group of up to 6 people, and an extra $25 per additional person if there are more than 6 people. The function f(n) , the total cost in dollars, depends on n , the number of people in the group. Assuming that there are at least 6 people in the group, which function correctly represents this situation?
A
f(n)=200(n−6)+25
B
f(n)=25n+200
C
f(n)=25(n−6)+200
D
f(n)=200n+25
Answer:
C
Step-by-step explanation:
Function that represents the situation correctly is f(n)=25(n−6)+200.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given, a photographer charges $200 to take photos of a group of up to 6 people, and an extra $25 per additional person if there are more than 6 people.
Let n= 6 means group of 6 people.
So substituting the value n= 6;
In the option A, f(6) = 25
In the option B , f(6) = 350
In the option C , f(6) = 200
In the option D , f(6) = 1225
Here, only option C matches with the given photographer's charges for 6 people.
Therefore, function that represents the situation correctly is f(n)=25(n−6)+200.
To learn more about the function;
brainly.com/question/28303908
#SPJ2
Is this right?? I think it is
pleasee help this is due
Answer:
Line across circle is diameter. Small line coming out of big line is radius. Line around circle is circumference.
Step-by-step explanation:
Ms.Knight wants to throw a pizza party for the 7th graders. In a random sample, 13 out of 20 7th graders preferred pepperoni pizza and the other 7 proffered cheese. Based on this data out of 400 total 7th graders approximately how many prefer pepperoni?
Give steps.
Answer:
260
Step-by-step explanation:
because 13 of 20 is 65% filled up and 260 is 65% of 400
Answer:
260 i say
Step-by-step explanation:
hi caroline
In ΔHIJ, the measure of ∠J=90°, the measure of ∠H=8°, and HI = 30 feet. Find the length of IJ to the nearest tenth of a foot.
Answer: 4.2
Step-by-step explanation:
Sin(H)=x/30 then cross multiply
30sin(8)=x
X=4.1752... but rounded it’s 4.2
Answer:
It's 4.2
Step-by-step explanation:
If ACD~ABE find the value of x
Step-by-step explanation:
I think it is a good day and the answer is 3
hii please help smart people
Answer:
x = 73 °
Step-by-step explanation:
A pentagon has a collective degree of 540
So to find x, you have to set up an equation:
x + 127 + 112 + 108 + 120 = 540
To solve:
Combine like terms
x + 467 = 540
Subtract 467 on both sides:
x = 540 - 467
x = 73
3. Graph the function.
xy + 25 = 0
Answer:
look at the answer below
Step-by-step explanation:
this is xy + 25 = 0 if you wanted it. hope it helps
Answer:
(Rational Functions Practice)
3. Graph the function. (1 point)
xy+25=0
Step-by-step explanation:
Graph B. is the correct answer
help please!! im so confused and this is a mid-term for a major grade!!
Answer:
the secend equation
[tex]y = - x + 9[/tex]
Step-by-step explanation:
If you need any explanation in it or anything on math you can communicate with me on Whats on this number +201557831028 or in email or face or anything.
I can help you solve what you want in mathematics in exchange for some money. If you want to, you can inform me about it and I will help you.
Formula is S=2nr squared
If r=7 and n=3.14,calculate S rounded off to two decimal places.
Answer:
307.72
Step-by-step explanation:
S=2nr²
S=2×3.14×7²
S=307.72
A savings account earns 8% interest each year, compounded quarterly (4 times a year). If a person invests $100 and makes no further deposits or withdrawals, what is the balance in the account after 3 years?
Answer:
251.817012
Step-by-step explanation:
1. Write out equation to get 100(1.08)^n*4
2. Use 3 for n
3. Simplify to get 100(1.08)^12
4. Solve to get 251.817012
Three girls share 12 000 in the ratio 2:3:7.Calculate how much each girl will get
Answer:
1st girl- 2000
2nd girl- 3000
3rd girl- 7000
Step-by-step explanation:
1) add the ratio given: 2+3+7=12
2) the answer that you get is the whole and it is equal to the total: 12/12=12000
3) so now you'll simplify to get the share of each girl: 12/12=12000, what about 2/12(for the first girl)
12/12=12000, what about 3/12(for the 2nd girl)
12/12=12000, what about 7/12(for the 3rd girl)
4) after getting the answer for each, you can add their shares to see if they are equivalent to the total share
a national park is a rectangle that is 33 miles wide and 56 miles long.how long is a diagonal road through the park
9514 1404 393
Answer:
65 miles
Step-by-step explanation:
The Pythagorean theorem applies.
d^2 = 33^2 +56^2
d^2 = 1089 +3136 = 4225
d = √4225 = 65
The diagonal road is 65 miles long.
What value for x will make the equation true?
−3 ( 7x − 5 ) = 87 + 3x
A. −17/4
B. -3
C. 4
D. 17/3
Answer:
C . 4
Step-by-step explanation:
step 1 : -3 multiply with inside of the ( 7x-5 )
= -21x + 15
step 2 : then it will be 21x + 15 = 87 + 3x
step 3 : switch between the odds into like this
21x - 3x = 87 - 15
step 4 : subtract it all
18x = 72
step 5 : bring 18 to the other side
x = 72/18
step 6 : to find the ans of x is just calculate them
x = 72 ÷ 18
= 4
Or you can do like these ⬇️
-3 ( 7x - 15 ) = 87 + 3x
21x + 15 = 87 + 3x
21x - 3x = 87 - 15
18x = 72
x = 72/18 or 72÷18
x = 4
Is 30 a typical test score? If so, explain your reasoning. If not, what is a typical test score?
Answer:
NO
Step-by-step explanation:
Failing a test is atypical for most kids. You have the occasional, but generally failing is something people don't really do. A typical test score varies from 95-70. It really just depends on the person. I sure hope you don't usually score 30's on tests.
stay cold,
brook
A number is 9 more than another number. Twice the sum of the two numbers is 10. Find the two numbers.
Step-by-step explanation:
the formula can be;
X+9x=10
10x=10X=10/10=1
X=1+9(1)=1+9=10 Answer
Will mark brainly
1,2,3,4, and 5 if you can:)
Answer:
1. A 2. B 3.D 4.C 5. E
Step-by-step explanation:
Consider this complex shape.
Which statements are true regarding the symmetries of this shape? Check all that apply.
OThe order of rotational symmetry is 3.
O Symmetry occurs after a rotation of 240º.
O The smallest angle of rotational symmetry is 180º.
O The figure has 3 lines of reflectional symmetry.
O Symmetry occurs after a rotation of 60º.
-The order of rotational symmetry is 3
- Symmetry occurs after a rotation of 240
- The figure has 3 lines of reflections symmetry
explanation: right on ed
Answer:
A B and D
Step-by-step explanation:
you're welcome
brainliest